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Volume 6 (2021): Issue 2 (July 2021)

Volume 6 (2021): Issue 1 (January 2021)

Volume 5 (2020): Issue 2 (July 2020)

Volume 5 (2020): Issue 1 (January 2020)

Volume 4 (2019): Issue 2 (July 2019)

Volume 4 (2019): Issue 1 (January 2019)

Volume 3 (2018): Issue 2 (July 2018)

Volume 3 (2018): Issue 1 (June 2018)

Volume 2 (2017): Issue 2 (July 2017)

Volume 2 (2017): Issue 1 (January 2017)

Volume 1 (2016): Issue 2 (July 2016)

Volume 1 (2016): Issue 1 (January 2016)

Journal Details
Format
Journal
eISSN
2444-8656
First Published
01 Jan 2016
Publication timeframe
2 times per year
Languages
English

Search

Volume 4 (2019): Issue 2 (July 2019)

Journal Details
Format
Journal
eISSN
2444-8656
First Published
01 Jan 2016
Publication timeframe
2 times per year
Languages
English

Search

25 Articles
Open Access

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Published Online: 01 Jul 2019
Page range: 289 - 304

Abstract

Abstract

In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.

Keywords

  • The (3+1)-dimensional space-time fractional mKdV–ZK
  • the variable separated ODE method
  • solitons and periodic wave solutions

MSC 2010

  • 35A24
  • 35C08
  • 35Q53
Open Access

Important Notes for a Fuzzy Boundary Value Problem

Published Online: 12 Aug 2019
Page range: 305 - 314

Abstract

Abstract

In this paper is studied a fuzzy Sturm-Liouville problem with the eigenvalue parameter in the boundary condition. Important notes are given for the problem. Integral equations are found of the problem.

Keywords

  • Fuzzy logic
  • Fuzzy Sturm-Liouville equation
  • Sturm-Liouville Theory

MSC 2010

  • Primary 03E72
  • Secondary 34B05
  • Thirth 34B24
Open Access

Dynamics of the Modified n-Degree Lorenz System

Published Online: 22 Aug 2019
Page range: 315 - 330

Abstract

Abstract

The Lorenz model is one of the most studied dynamical systems. Chaotic dynamics of several modified models of the classical Lorenz system are studied. In this article, a new chaotic model is introduced and studied computationally. By finding the fixed points, the eigenvalues of the Jacobian, and the Lyapunov exponents. Transition from convergence behavior to the periodic behavior (limit cycle) are observed by varying the degree of the system. Also transiting from periodic behavior to the chaotic behavior are seen by changing the degree of the system.

Keywords

  • Modified Chaotic System
  • Chaos
  • Periodic
  • Lorenz System & Dynamical Systems

MSC 2010

  • 39A10
  • 39A11
Open Access

Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

Published Online: 23 Aug 2019
Page range: 331 - 350

Abstract

Abstract

In this paper non-convexity in economics has been revisited. Shapley-Folkman-Lyapunov theorem has been tested with the asymmetric auctions where bidders follow log-concave probability distributions (non-convex preferences). Ten standard statistical distributions have been used to describe the bidders’ behavior. In principle what is been tested is that equilibrium price can be achieved where the sum of large number non-convex sets is convex (approximately), so that optimization is possible. Convexity is thus very important in economics.

Keywords

  • Shapley-Folkman theorem
  • asymmetric auctions
  • Backward shooting method
  • auction solving
  • fixed point iterations

MSC 2010

  • C65
  • D44
Open Access

Application of modified wavelet and homotopy perturbation methods to nonlinear oscillation problems

Published Online: 23 Aug 2019
Page range: 351 - 364

Abstract

Abstract

In this paper, an accurate and efficient Chebyshev wavelet-based technique is successfully employed to solve the nonlinear oscillation problems. Numerical examples are also provided to illustrate the efficiency and performance of these methods. Homotopy perturbation methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations. In addition, the use of Chebyshev wavelet is found to be simple, flexible, accurate, efficient and less computational cost. Our analytical results are compared with simulation results and found to be satisfactory.

Keywords

  • Chebyshev wavelet
  • nonlinear oscillation
  • homotopy perturbation
  • operational matrix
  • numerical solutions

MSC 2010

  • 34E10
  • 34E13
  • 35K20
  • 35K60
Open Access

New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

Published Online: 30 Aug 2019
Page range: 365 - 370

Abstract

Abstract

In this study, we use the improved Bernoulli sub-equation function method for exact solutions to the generalized (3+1) shallow water-like (SWL) equation. Some new solutions are successfully constructed. We carried out all the computations and the graphics plot in this paper by Wolfram Mathematica.

Keywords

  • Generalized (3+1) shallow water-like (SWL) equation
  • Improved Bernoulli sub-equation function method
  • Exact solution

MSC 2010

  • 35Q35
  • 37N10
Open Access

QSPR Analysis of certain Distance Based Topological Indices

Published Online: 27 Sep 2019
Page range: 371 - 386

Abstract

Abstract

In QSAR/QSPR study, topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we study the QSPR analysis of selected distance and degree-distance based topological indices. Our study reveals some important results which help us to characterize the useful topological indices based on their predicting power.

Keywords

  • Distance
  • Degree-Distance
  • QSPR

MSC 2010

  • 05C90
  • 05C35
  • 05C12
Open Access

Multidimensional BSDE with Poisson jumps of Osgood type

Published Online: 01 Oct 2019
Page range: 387 - 394

Abstract

Abstract

This paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under linear growth generator, we prove existence and uniqueness of solution.

Keywords

  • Backward stochastic differential equation
  • random Poisson measure

MSC 2010

  • 60H05
  • 60G44
Open Access

Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

Published Online: 25 Oct 2019
Page range: 395 - 406

Abstract

Abstract

A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

Keywords

  • Abel′s integral equations
  • Hermite wavelets
  • collocation method

MSC 2010

  • 65T60
  • 65R20
  • 97N40
Open Access

Investigation of A Fuzzy Problem by the Fuzzy Laplace Transform

Published Online: 28 Oct 2019
Page range: 407 - 416

Abstract

Abstract

This paper is on the solutions of a fuzzy problem with triangular fuzzy number initial values by fuzzy Laplace transform. In this paper, the properties of fuzzy Laplace transform, generalized differentiability and fuzzy arithmetic are used. The example is solved in relation to the studied problem. Conclusions are given.

Keywords

  • Fuzzy logic
  • Fuzzy differential equation
  • Fuzzy Laplace Transform

MSC 2010

  • 03E72
  • 44A10
Open Access

A New Approach For Weighted Hardy’s Operator In VELS

Published Online: 28 Oct 2019
Page range: 417 - 432

Abstract

Abstract

A considerable number of research has been carried out on the generalized Lebesgue spaces Lp(x) and boundedness of different integral operators therein. In this study, a new approach for weighted increasing near the origin and decreasing near infinity exponent function that provides a boundedness of the Hardy’s operator in variable exponent space is given.

Keywords

  • Hardy inequality
  • Variable exponent
  • Boundedness

MSC 2010

  • 42A05
  • 42B35
  • 26D10
Open Access

Fully discrete convergence analysis of non-linear hyperbolic equations based on finite element analysis

Published Online: 08 Nov 2019
Page range: 433 - 444

Abstract

Abstract

With the development of modern partial differential equation (PDE) theory, the theory of linear PDE is becoming more and more perfect, . Non-linear PDE has become a research hotspot of many mathematicians. In fact, when describing practical physical problems with PDEs, non-linear problems tend to be more general than linear problems, which are close to real problems and have practical physical significance. Hyperbolic PDEs are a kind of important PDEs describing the phenomena of vibration or wave motion. The solution of hyperbolic PDE can be decomposed into the form of multiplication of vibration and vibration or of exponential function and exponential function. Generally, the energy is infinite. A full discrete convergence analysis method for non-linear hyperbolic equation based on finite element analysis is proposed. Taking second-order and fourth-order non-linear hyperbolic equation as examples, the full discrete convergence of non-linear hyperbolic equation is analysed by finite element method and the super-convergence results are obtained.

Keywords

  • finite element analysis
  • nonlinearity
  • hyperbolic equation
  • fully discrete
  • convergence
  • error
Open Access

Word series high-order averaging of highly oscillatory differential equations with delay

Published Online: 20 Dec 2019
Page range: 445 - 454

Abstract

Abstract

We show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order averaged equations for differential equations without delay.

Keywords

  • Delay differential equations
  • stroboscopic averaging
  • word series

MSC 2010

  • 34C29
Open Access

Computation of certain topological coindices of graphene sheet and C4C8(S) nanotubes and nanotorus

Published Online: 18 Dec 2019
Page range: 455 - 468

Abstract

Abstract

Topological indices are widely used for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). Topological coindices are topological indices that considers the non adjacent pairs of vertices. Here, we consider the following five well-known topological coindices: the first and second Zagreb coindices, the first and second multiplicative Zagreb coindices and the F-coindex. By using graph structural analysis and derivation, we study the above-mentioned topological coindices of some chemical molecular graphs that frequently appear in medical, chemical, and material engineering such as graphene sheet and C4C8(S) nanotubes and nanotorus and obtain the computation formulae of the coindices of these graphs. Furthermore, we analyze the results by MATLAB and obtain the relationship of the coindices which they describe the physcio-chemical properties and biological activities.

Keywords

  • Molecular graph
  • topological coindex
  • graphene sheet
  • nanotubes
  • nanotorus

MSC 2010

  • 05C90
  • 90C35
Open Access

Identification of the initial temperature from the given temperature data at the left end of a rod

Published Online: 18 Dec 2019
Page range: 469 - 474

Abstract

Abstract

This study aims to investigate the problem of determining the unknown initial temperature in a variable coefficient heat equation. We obtain the existence and uniqueness of the solution of the optimal control problem considered under some conditions. Using the adjoint problem approach, we get the Frechet differential of the cost functional. We construct a minimizing sequence and give the convergence rate of this sequence. Also, we test the theoretical results in a numerical example by using the MAPLE® program.

Keywords

  • Optimal Control
  • Frechet Differential
  • Adjoint Approach

MSC 2010

  • 49J20
  • 49J50
Open Access

Soret and Dufour effects on chemically reacting mixed convection flow in an annulus with Navier slip and convective boundary conditions

Published Online: 18 Dec 2019
Page range: 475 - 488

Abstract

Abstract

This analysis is to study the incompressible mixed convection laminar Newtonian flow through concentric cylindrical annulus associated with slip and convective boundary conditions. This presentation considered the cross diffusions and chemical reaction effects also. The fluid flow in an annulus is due to the rotation of the outer cylinder with constant velocity. The analysis of such kind of fluid flow is governed by nonlinear partial differential equations. The governing system of equations were mapped into dimensionless system with appropriate transformations. The system has been solved using Homotopy Analysis Method (HAM). The influence of Soret, Dufour, slip parameter and the chemical reaction parameter on velocity, temperature and concentration are investigated, and presented through plots. The maximum values of slip leads to increase in velocity and temperature profiles. Further the impact of boundary conditions on velocity, temperature and concentration are also presented.

Keywords

  • Mixed Convection
  • cross diffusion effects
  • Chemical reaction
  • convective boundary
  • Navier slip
  • HAM

MSC 2010

  • 76D05
  • 76E06
  • 65H20
  • 76V05
Open Access

Yang-Laplace Decomposition Method for Nonlinear System of Local Fractional Partial Differential Equations

Published Online: 24 Dec 2019
Page range: 489 - 502

Abstract

Abstract

The basic motivation of the present study is to extend the application of the local fractional Yang-Laplace decomposition method to solve nonlinear systems of local fractional partial differential equations. The differential operators are taken in the local fractional sense. The local fractional Yang-Laplace decomposition method (LFLDM) can be easily applied to many problems and is capable of reducing the size of computational work to find non-differentiable solutions for similar problems. Two illustrative examples are given, revealing the effectiveness and convenience of the method.

Keywords

  • Local fractional derivative operator
  • local fractional Yang-Laplace decomposition method
  • nonlinear systems of local fractional partial differential equations

MSC 2010

  • 49K20
Open Access

On graphs with equal dominating and c-dominating energy

Published Online: 24 Dec 2019
Page range: 503 - 512

Abstract

Abstract

Graph energy and domination in graphs are most studied areas of graph theory. In this paper we try to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.

Keywords

  • Dominating set
  • Connected dominating set
  • Energy
  • Dominating energy
  • c-Dominating energy

MSC 2010

  • 05C69
  • 05C90
  • 05C35
  • 05C12
Open Access

The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model

Published Online: 24 Dec 2019
Page range: 513 - 522

Abstract

Abstract

This work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given.

Keywords

  • New extended rational SGEEM
  • KMN model
  • optical solitons

MSC 2010

  • 49K20
Open Access

Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

Published Online: 24 Dec 2019
Page range: 523 - 534

Abstract

Abstract

In this article, we attain new analytical solution sets for nonlinear time-fractional coupled Burgers’ equations which arise in polydispersive sedimentation in shallow water waves using exp-function method. Then we apply a semi-analytical method namely perturbation-iteration algorithm (PIA) to obtain some approximate solutions. These results are compared with obtained exact solutions by tables and surface plots. The fractional derivatives are evaluated in the conformable sense. The findings reveal that both methods are very effective and dependable for solving partial fractional differential equations.

Keywords

  • Fractional Coupled Burger’s Equation
  • Conformable Fractional Derivative
  • Perturbation-Iteration Algorithm
  • Exp-Function Method

MSC 2010

  • 35R11
  • 35A20
  • 35C05
Open Access

Optical solitons to the fractional Schrödinger-Hirota equation

Published Online: 26 Dec 2019
Page range: 535 - 542

Abstract

Abstract

This study reaches the dark, bright, mixed dark-bright, and singular optical solitons to the fractional Schrödinger-Hirota equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. Dark soliton describes the solitary waves with lower intensity than the background, bright soliton describes the solitary waves whose peak intensity is larger than the background, and the singular soliton solutions is a solitary wave with discontinuous derivatives; examples of such solitary waves include compactions, which have finite (compact) support, and peakons, whose peaks have a discontinuous first derivative. The constraint conditions for the existence of valid solutions are given. We use some suitable values of the parameters in plotting 3-dimensional surfaces to some of the reported solutions.

Keywords

  • M-fractional derivative
  • sinh-Gordon equation
  • Schrdinger-Hirota equation
  • optical soliton

MSC 2010

  • 49K20
Open Access

Note On Jakimovski-Leviatan Operators Preserving ex

Published Online: 26 Dec 2019
Page range: 543 - 550

Abstract

Abstract

In the present article, a modification of Jakimovski-Leviatan operators is presented which reproduce constant and ex functions. We prove uniform convergence order of a quantitative estimate for the modified operators. We also give a quantitative Voronovskya type theorem.

Keywords

  • Jakimovski-Leviatan operators
  • Exponential functions
  • Quantitative asymptotic formula
  • Uniform convergence
  • Voronovskya type theorem

MSC 2010

  • 41A10
  • 41A25
  • 41A36
Open Access

Mathematical analysis of a B-cell chronic lymphocytic leukemia model with immune response

Published Online: 26 Dec 2019
Page range: 551 - 558

Abstract

Abstract

A B-cell chronic lymphocytic leukemia has been modeled via a highly nonlinear system of ordinary differential equations. We consider the rather important theoretical question of the equilibria existence. Under suitable assumptions all model populations are shown to coexist.

Keywords

  • Leukemia
  • Descartes rule
  • Local stability

MSC 2010

  • AMS 2010 MSC primary
  • 92D40
  • secondary
  • 92D25
  • 92D30
Open Access

New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in Banach spaces

Published Online: 26 Dec 2019
Page range: 559 - 574

Abstract

Abstract

In this paper, we suggest and analyze a new iterative method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of fixed points of a demicontractive mapping which is the unique solution of some variational inequality problems involving accretive operators in a Banach space. We prove the strong convergence of the proposed iterative scheme without imposing any compactness condition on the mapping or the space. Finally, applications of our theorems to some constrained convex minimization problems are given.

Keywords

  • Demicontractive mappings
  • Quasi-nonexpansive mappings
  • Common fixed points
  • Accretive operators

MSC 2010

  • 47H05
  • 47H09
  • 47J25
Open Access

Entropy Generation in Couette Flow Through a Deformable Porous Channel

Published Online: 26 Dec 2019
Page range: 575 - 590

Abstract

Abstract

The present study examines the entropy generation on Couette flow of a viscous fluid in parallel plates filled with deformable porous medium. The fluid is injected into the porous channel perpendicular to the lower wall with a constant velocity and is sucked out of the upper wall with same velocity .The coupled phenomenon of the fluid flow and solid deformation in the porous medium is taken in to consideration. The exact expressions for the velocity of fluid, solid displacement and temperature distribution are found analytically. The effect of pertinent parameters on the fluid velocity, solid displacement and temperature profiles are discussed in detail. In the deformable porous layer, it is noticed that the velocity of fluid, solid displacement and temperature distribution are decreases with increasing the suction/injection velocity parameter. The results obtained for the present flow characteristic reveal several interesting behaviors that warrant further study on the deformable porous media. Furthermore, the significance of drag and the volume fraction on entropy generation number and Bejan number are discussed with the help of graphs.

Keywords

  • Couette flow
  • deformable porous layer
  • suction/injection
  • entropy generation
  • Bejan number

MSC 2010

  • 76S05
25 Articles
Open Access

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Published Online: 01 Jul 2019
Page range: 289 - 304

Abstract

Abstract

In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.

Keywords

  • The (3+1)-dimensional space-time fractional mKdV–ZK
  • the variable separated ODE method
  • solitons and periodic wave solutions

MSC 2010

  • 35A24
  • 35C08
  • 35Q53
Open Access

Important Notes for a Fuzzy Boundary Value Problem

Published Online: 12 Aug 2019
Page range: 305 - 314

Abstract

Abstract

In this paper is studied a fuzzy Sturm-Liouville problem with the eigenvalue parameter in the boundary condition. Important notes are given for the problem. Integral equations are found of the problem.

Keywords

  • Fuzzy logic
  • Fuzzy Sturm-Liouville equation
  • Sturm-Liouville Theory

MSC 2010

  • Primary 03E72
  • Secondary 34B05
  • Thirth 34B24
Open Access

Dynamics of the Modified n-Degree Lorenz System

Published Online: 22 Aug 2019
Page range: 315 - 330

Abstract

Abstract

The Lorenz model is one of the most studied dynamical systems. Chaotic dynamics of several modified models of the classical Lorenz system are studied. In this article, a new chaotic model is introduced and studied computationally. By finding the fixed points, the eigenvalues of the Jacobian, and the Lyapunov exponents. Transition from convergence behavior to the periodic behavior (limit cycle) are observed by varying the degree of the system. Also transiting from periodic behavior to the chaotic behavior are seen by changing the degree of the system.

Keywords

  • Modified Chaotic System
  • Chaos
  • Periodic
  • Lorenz System & Dynamical Systems

MSC 2010

  • 39A10
  • 39A11
Open Access

Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

Published Online: 23 Aug 2019
Page range: 331 - 350

Abstract

Abstract

In this paper non-convexity in economics has been revisited. Shapley-Folkman-Lyapunov theorem has been tested with the asymmetric auctions where bidders follow log-concave probability distributions (non-convex preferences). Ten standard statistical distributions have been used to describe the bidders’ behavior. In principle what is been tested is that equilibrium price can be achieved where the sum of large number non-convex sets is convex (approximately), so that optimization is possible. Convexity is thus very important in economics.

Keywords

  • Shapley-Folkman theorem
  • asymmetric auctions
  • Backward shooting method
  • auction solving
  • fixed point iterations

MSC 2010

  • C65
  • D44
Open Access

Application of modified wavelet and homotopy perturbation methods to nonlinear oscillation problems

Published Online: 23 Aug 2019
Page range: 351 - 364

Abstract

Abstract

In this paper, an accurate and efficient Chebyshev wavelet-based technique is successfully employed to solve the nonlinear oscillation problems. Numerical examples are also provided to illustrate the efficiency and performance of these methods. Homotopy perturbation methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations. In addition, the use of Chebyshev wavelet is found to be simple, flexible, accurate, efficient and less computational cost. Our analytical results are compared with simulation results and found to be satisfactory.

Keywords

  • Chebyshev wavelet
  • nonlinear oscillation
  • homotopy perturbation
  • operational matrix
  • numerical solutions

MSC 2010

  • 34E10
  • 34E13
  • 35K20
  • 35K60
Open Access

New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

Published Online: 30 Aug 2019
Page range: 365 - 370

Abstract

Abstract

In this study, we use the improved Bernoulli sub-equation function method for exact solutions to the generalized (3+1) shallow water-like (SWL) equation. Some new solutions are successfully constructed. We carried out all the computations and the graphics plot in this paper by Wolfram Mathematica.

Keywords

  • Generalized (3+1) shallow water-like (SWL) equation
  • Improved Bernoulli sub-equation function method
  • Exact solution

MSC 2010

  • 35Q35
  • 37N10
Open Access

QSPR Analysis of certain Distance Based Topological Indices

Published Online: 27 Sep 2019
Page range: 371 - 386

Abstract

Abstract

In QSAR/QSPR study, topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we study the QSPR analysis of selected distance and degree-distance based topological indices. Our study reveals some important results which help us to characterize the useful topological indices based on their predicting power.

Keywords

  • Distance
  • Degree-Distance
  • QSPR

MSC 2010

  • 05C90
  • 05C35
  • 05C12
Open Access

Multidimensional BSDE with Poisson jumps of Osgood type

Published Online: 01 Oct 2019
Page range: 387 - 394

Abstract

Abstract

This paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under linear growth generator, we prove existence and uniqueness of solution.

Keywords

  • Backward stochastic differential equation
  • random Poisson measure

MSC 2010

  • 60H05
  • 60G44
Open Access

Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

Published Online: 25 Oct 2019
Page range: 395 - 406

Abstract

Abstract

A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

Keywords

  • Abel′s integral equations
  • Hermite wavelets
  • collocation method

MSC 2010

  • 65T60
  • 65R20
  • 97N40
Open Access

Investigation of A Fuzzy Problem by the Fuzzy Laplace Transform

Published Online: 28 Oct 2019
Page range: 407 - 416

Abstract

Abstract

This paper is on the solutions of a fuzzy problem with triangular fuzzy number initial values by fuzzy Laplace transform. In this paper, the properties of fuzzy Laplace transform, generalized differentiability and fuzzy arithmetic are used. The example is solved in relation to the studied problem. Conclusions are given.

Keywords

  • Fuzzy logic
  • Fuzzy differential equation
  • Fuzzy Laplace Transform

MSC 2010

  • 03E72
  • 44A10
Open Access

A New Approach For Weighted Hardy’s Operator In VELS

Published Online: 28 Oct 2019
Page range: 417 - 432

Abstract

Abstract

A considerable number of research has been carried out on the generalized Lebesgue spaces Lp(x) and boundedness of different integral operators therein. In this study, a new approach for weighted increasing near the origin and decreasing near infinity exponent function that provides a boundedness of the Hardy’s operator in variable exponent space is given.

Keywords

  • Hardy inequality
  • Variable exponent
  • Boundedness

MSC 2010

  • 42A05
  • 42B35
  • 26D10
Open Access

Fully discrete convergence analysis of non-linear hyperbolic equations based on finite element analysis

Published Online: 08 Nov 2019
Page range: 433 - 444

Abstract

Abstract

With the development of modern partial differential equation (PDE) theory, the theory of linear PDE is becoming more and more perfect, . Non-linear PDE has become a research hotspot of many mathematicians. In fact, when describing practical physical problems with PDEs, non-linear problems tend to be more general than linear problems, which are close to real problems and have practical physical significance. Hyperbolic PDEs are a kind of important PDEs describing the phenomena of vibration or wave motion. The solution of hyperbolic PDE can be decomposed into the form of multiplication of vibration and vibration or of exponential function and exponential function. Generally, the energy is infinite. A full discrete convergence analysis method for non-linear hyperbolic equation based on finite element analysis is proposed. Taking second-order and fourth-order non-linear hyperbolic equation as examples, the full discrete convergence of non-linear hyperbolic equation is analysed by finite element method and the super-convergence results are obtained.

Keywords

  • finite element analysis
  • nonlinearity
  • hyperbolic equation
  • fully discrete
  • convergence
  • error
Open Access

Word series high-order averaging of highly oscillatory differential equations with delay

Published Online: 20 Dec 2019
Page range: 445 - 454

Abstract

Abstract

We show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order averaged equations for differential equations without delay.

Keywords

  • Delay differential equations
  • stroboscopic averaging
  • word series

MSC 2010

  • 34C29
Open Access

Computation of certain topological coindices of graphene sheet and C4C8(S) nanotubes and nanotorus

Published Online: 18 Dec 2019
Page range: 455 - 468

Abstract

Abstract

Topological indices are widely used for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). Topological coindices are topological indices that considers the non adjacent pairs of vertices. Here, we consider the following five well-known topological coindices: the first and second Zagreb coindices, the first and second multiplicative Zagreb coindices and the F-coindex. By using graph structural analysis and derivation, we study the above-mentioned topological coindices of some chemical molecular graphs that frequently appear in medical, chemical, and material engineering such as graphene sheet and C4C8(S) nanotubes and nanotorus and obtain the computation formulae of the coindices of these graphs. Furthermore, we analyze the results by MATLAB and obtain the relationship of the coindices which they describe the physcio-chemical properties and biological activities.

Keywords

  • Molecular graph
  • topological coindex
  • graphene sheet
  • nanotubes
  • nanotorus

MSC 2010

  • 05C90
  • 90C35
Open Access

Identification of the initial temperature from the given temperature data at the left end of a rod

Published Online: 18 Dec 2019
Page range: 469 - 474

Abstract

Abstract

This study aims to investigate the problem of determining the unknown initial temperature in a variable coefficient heat equation. We obtain the existence and uniqueness of the solution of the optimal control problem considered under some conditions. Using the adjoint problem approach, we get the Frechet differential of the cost functional. We construct a minimizing sequence and give the convergence rate of this sequence. Also, we test the theoretical results in a numerical example by using the MAPLE® program.

Keywords

  • Optimal Control
  • Frechet Differential
  • Adjoint Approach

MSC 2010

  • 49J20
  • 49J50
Open Access

Soret and Dufour effects on chemically reacting mixed convection flow in an annulus with Navier slip and convective boundary conditions

Published Online: 18 Dec 2019
Page range: 475 - 488

Abstract

Abstract

This analysis is to study the incompressible mixed convection laminar Newtonian flow through concentric cylindrical annulus associated with slip and convective boundary conditions. This presentation considered the cross diffusions and chemical reaction effects also. The fluid flow in an annulus is due to the rotation of the outer cylinder with constant velocity. The analysis of such kind of fluid flow is governed by nonlinear partial differential equations. The governing system of equations were mapped into dimensionless system with appropriate transformations. The system has been solved using Homotopy Analysis Method (HAM). The influence of Soret, Dufour, slip parameter and the chemical reaction parameter on velocity, temperature and concentration are investigated, and presented through plots. The maximum values of slip leads to increase in velocity and temperature profiles. Further the impact of boundary conditions on velocity, temperature and concentration are also presented.

Keywords

  • Mixed Convection
  • cross diffusion effects
  • Chemical reaction
  • convective boundary
  • Navier slip
  • HAM

MSC 2010

  • 76D05
  • 76E06
  • 65H20
  • 76V05
Open Access

Yang-Laplace Decomposition Method for Nonlinear System of Local Fractional Partial Differential Equations

Published Online: 24 Dec 2019
Page range: 489 - 502

Abstract

Abstract

The basic motivation of the present study is to extend the application of the local fractional Yang-Laplace decomposition method to solve nonlinear systems of local fractional partial differential equations. The differential operators are taken in the local fractional sense. The local fractional Yang-Laplace decomposition method (LFLDM) can be easily applied to many problems and is capable of reducing the size of computational work to find non-differentiable solutions for similar problems. Two illustrative examples are given, revealing the effectiveness and convenience of the method.

Keywords

  • Local fractional derivative operator
  • local fractional Yang-Laplace decomposition method
  • nonlinear systems of local fractional partial differential equations

MSC 2010

  • 49K20
Open Access

On graphs with equal dominating and c-dominating energy

Published Online: 24 Dec 2019
Page range: 503 - 512

Abstract

Abstract

Graph energy and domination in graphs are most studied areas of graph theory. In this paper we try to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.

Keywords

  • Dominating set
  • Connected dominating set
  • Energy
  • Dominating energy
  • c-Dominating energy

MSC 2010

  • 05C69
  • 05C90
  • 05C35
  • 05C12
Open Access

The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model

Published Online: 24 Dec 2019
Page range: 513 - 522

Abstract

Abstract

This work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given.

Keywords

  • New extended rational SGEEM
  • KMN model
  • optical solitons

MSC 2010

  • 49K20
Open Access

Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

Published Online: 24 Dec 2019
Page range: 523 - 534

Abstract

Abstract

In this article, we attain new analytical solution sets for nonlinear time-fractional coupled Burgers’ equations which arise in polydispersive sedimentation in shallow water waves using exp-function method. Then we apply a semi-analytical method namely perturbation-iteration algorithm (PIA) to obtain some approximate solutions. These results are compared with obtained exact solutions by tables and surface plots. The fractional derivatives are evaluated in the conformable sense. The findings reveal that both methods are very effective and dependable for solving partial fractional differential equations.

Keywords

  • Fractional Coupled Burger’s Equation
  • Conformable Fractional Derivative
  • Perturbation-Iteration Algorithm
  • Exp-Function Method

MSC 2010

  • 35R11
  • 35A20
  • 35C05
Open Access

Optical solitons to the fractional Schrödinger-Hirota equation

Published Online: 26 Dec 2019
Page range: 535 - 542

Abstract

Abstract

This study reaches the dark, bright, mixed dark-bright, and singular optical solitons to the fractional Schrödinger-Hirota equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. Dark soliton describes the solitary waves with lower intensity than the background, bright soliton describes the solitary waves whose peak intensity is larger than the background, and the singular soliton solutions is a solitary wave with discontinuous derivatives; examples of such solitary waves include compactions, which have finite (compact) support, and peakons, whose peaks have a discontinuous first derivative. The constraint conditions for the existence of valid solutions are given. We use some suitable values of the parameters in plotting 3-dimensional surfaces to some of the reported solutions.

Keywords

  • M-fractional derivative
  • sinh-Gordon equation
  • Schrdinger-Hirota equation
  • optical soliton

MSC 2010

  • 49K20
Open Access

Note On Jakimovski-Leviatan Operators Preserving ex

Published Online: 26 Dec 2019
Page range: 543 - 550

Abstract

Abstract

In the present article, a modification of Jakimovski-Leviatan operators is presented which reproduce constant and ex functions. We prove uniform convergence order of a quantitative estimate for the modified operators. We also give a quantitative Voronovskya type theorem.

Keywords

  • Jakimovski-Leviatan operators
  • Exponential functions
  • Quantitative asymptotic formula
  • Uniform convergence
  • Voronovskya type theorem

MSC 2010

  • 41A10
  • 41A25
  • 41A36
Open Access

Mathematical analysis of a B-cell chronic lymphocytic leukemia model with immune response

Published Online: 26 Dec 2019
Page range: 551 - 558

Abstract

Abstract

A B-cell chronic lymphocytic leukemia has been modeled via a highly nonlinear system of ordinary differential equations. We consider the rather important theoretical question of the equilibria existence. Under suitable assumptions all model populations are shown to coexist.

Keywords

  • Leukemia
  • Descartes rule
  • Local stability

MSC 2010

  • AMS 2010 MSC primary
  • 92D40
  • secondary
  • 92D25
  • 92D30
Open Access

New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in Banach spaces

Published Online: 26 Dec 2019
Page range: 559 - 574

Abstract

Abstract

In this paper, we suggest and analyze a new iterative method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of fixed points of a demicontractive mapping which is the unique solution of some variational inequality problems involving accretive operators in a Banach space. We prove the strong convergence of the proposed iterative scheme without imposing any compactness condition on the mapping or the space. Finally, applications of our theorems to some constrained convex minimization problems are given.

Keywords

  • Demicontractive mappings
  • Quasi-nonexpansive mappings
  • Common fixed points
  • Accretive operators

MSC 2010

  • 47H05
  • 47H09
  • 47J25
Open Access

Entropy Generation in Couette Flow Through a Deformable Porous Channel

Published Online: 26 Dec 2019
Page range: 575 - 590

Abstract

Abstract

The present study examines the entropy generation on Couette flow of a viscous fluid in parallel plates filled with deformable porous medium. The fluid is injected into the porous channel perpendicular to the lower wall with a constant velocity and is sucked out of the upper wall with same velocity .The coupled phenomenon of the fluid flow and solid deformation in the porous medium is taken in to consideration. The exact expressions for the velocity of fluid, solid displacement and temperature distribution are found analytically. The effect of pertinent parameters on the fluid velocity, solid displacement and temperature profiles are discussed in detail. In the deformable porous layer, it is noticed that the velocity of fluid, solid displacement and temperature distribution are decreases with increasing the suction/injection velocity parameter. The results obtained for the present flow characteristic reveal several interesting behaviors that warrant further study on the deformable porous media. Furthermore, the significance of drag and the volume fraction on entropy generation number and Bejan number are discussed with the help of graphs.

Keywords

  • Couette flow
  • deformable porous layer
  • suction/injection
  • entropy generation
  • Bejan number

MSC 2010

  • 76S05