Rivista e Edizione

Volume 80 (2021): Edizione 3 (December 2021)

Volume 79 (2021): Edizione 2 (December 2021)

Volume 78 (2021): Edizione 1 (October 2021)

Volume 77 (2020): Edizione 1 (December 2020)

Volume 76 (2020): Edizione 1 (December 2020)
Real Functions, Dynamical Systems and their Applications

Volume 75 (2020): Edizione 1 (April 2020)
Applied Mathematics'19

Volume 74 (2019): Edizione 1 (December 2019)
Real Functons, Ideals, Measurable Functions, Functional Equations

Volume 73 (2019): Edizione 1 (August 2019)
Number Theory, Algebra and Cryptology '18

Volume 72 (2018): Edizione 1 (December 2018)

Volume 71 (2018): Edizione 1 (December 2018)

Volume 70 (2017): Edizione 1 (September 2017)

Volume 69 (2017): Edizione 1 (June 2017)

Volume 68 (2017): Edizione 1 (March 2017)
Special Edizione: Real Functions ’16, Real Functions, Density Topologies, Porosity

Volume 67 (2016): Edizione 1 (September 2016)

Volume 66 (2016): Edizione 1 (June 2016)
Edizione title: Applied Mathematics ’16

Volume 65 (2016): Edizione 1 (March 2016)
Real Functions '15 — Measure Theory, Real Functions, General Topology. Editors: J. Borsík, 2016.

Volume 64 (2015): Edizione 1 (September 2015)
Number Theory and Cryptology ’15

Volume 62 (2015): Edizione 1 (March 2015)
Special Edizione Title: Real Functions ’14

Volume 61 (2014): Edizione 1 (December 2014)
Special Edizione Title: Applied Mathematics ‘14

Volume 60 (2014): Edizione 1 (September 2014)
Special Edizione Title: Cryptology ’14

Volume 59 (2014): Edizione 1 (June 2014)
Special Edizione Title: Number Theory ‘14

Volume 58 (2014): Edizione 1 (March 2014)
Real Functions ‘13 Real Functions, Topology, Real and Functional Analysis, Locally Convex Spaces

Volume 57 (2013): Edizione 1 (December 2013)
Cryptology

Volume 56 (2013): Edizione 1 (November 2013)
Number Theory

Volume 55 (2013): Edizione 1 (August 2013)

Volume 54 (2013): Edizione 1 (April 2013)
Differential and Difference Equations and Applications ‘2012

Volume 53 (2012): Edizione 1 (December 2012)
TATRACRYPT ‘12

Volume 52 (2012): Edizione 1 (August 2012)

Volume 51 (2012): Edizione 1 (April 2012)
PROBASTAT ‘11

Volume 50 (2011): Edizione 1 (December 2011)
Applied Mathematics and Informatics

Volume 49 (2011): Edizione 1 (August 2011)
Real Functions ‘10

Volume 48 (2011): Edizione 1 (April 2011)
Differential and Difference Equations and Applications 2010

Volume 47 (2010): Edizione 1 (December 2010)
CCEC ‘09

Volume 46 (2010): Edizione 1 (August 2010)
Real Functions ‘09

Volume 45 (2010): Edizione 1 (April 2010)
NILCRYPT ‘10

Volume 44 (2009): Edizione 1 (December 2009)
Real Function ’08 Functional Equation, Measures, Integration and Harmonic Analysis

Volume 43 (2009): Edizione 1 (August 2009)
Differential and Difference Equations and Applications 2008

Volume 42 (2009): Edizione 1 (April 2009)
Real Function ‘07

Dettagli della rivista
Formato
Rivista
eISSN
1338-9750
Pubblicato per la prima volta
12 Nov 2012
Periodo di pubblicazione
3 volte all'anno
Lingue
Inglese

Cerca

Volume 79 (2021): Edizione 2 (December 2021)

Dettagli della rivista
Formato
Rivista
eISSN
1338-9750
Pubblicato per la prima volta
12 Nov 2012
Periodo di pubblicazione
3 volte all'anno
Lingue
Inglese

Cerca

12 Articoli
Accesso libero

Application of the Extended Fan Sub-Equation Method to Time Fractional Burgers-Fisher Equation

Pubblicato online: 01 Jan 2022
Pagine: 1 - 12

Astratto

Abstract

In this paper, the extended Fan sub-equation method to obtain the exact solutions of the generalized time fractional Burgers-Fisher equation is applied. By applying this method, we obtain different solutions that are benefit to further comprise the concepts of complex nonlinear physical phenomena. This method is simple and can be applied to several nonlinear equations. Fractional derivatives are taken in the sense of Jumarie’s modified Riemann-Liouville derivative. A comparative study with the other methods approves the validity and effectiveness of the technique, and on the other hand, for suitable parameter values, we plot 2D and 3D graphics of the exact solutions by using the extended Fan sub-equation method. In this work, we use Mathematica for computations and programming.

Parole chiave

  • extended Fan sub-equation method
  • time fractional Burgers-Fisher equation
  • solitary wave solution
Accesso libero

Some Results Involving the Airy Functions and Airy Transforms

Pubblicato online: 01 Jan 2022
Pagine: 13 - 32

Astratto

Abstract

In the present work, the author studied some properties of the modified Bessel’s functions and Airy functions. It is worth mentioning that the Airy functions are used in many fields of physics. They are applied in many branches of classical and quantum physics. The author also studied certain properties of the Airy transform and derived some new integral relations involving the Airy functions. Non-trivial illustrative examples are provided as well. All the results are presented in lucid and comprehensible language.

Parole chiave

  • Airy function
  • Airy transform
  • modified Bessel functions
  • Riccati differential equation
  • Parseval-Plancherel identity
Accesso libero

Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point

Pubblicato online: 01 Jan 2022
Pagine: 33 - 46

Astratto

Abstract

The problems of existence of limit cycles and their numbers are the most difficult problems in the dynamical planar systems. In this paper, we study the limit cycles for a family of polynomial differential systems of degree 6k + 1, k ∈ ℕ*, with the non-elementary singular point. Under some suitable conditions, we show our system exhibiting two non algebraic or two algebraic limit cycles explicitly given. To illustrate our results we present some examples.

Parole chiave

  • Algebraic and non–algebraic limit cycle
  • planar polynomial differential system
  • first integral
Accesso libero

Explicit Non Algebraic Limit Cycle for a Discontinuous Piecewise Differential Systems Separated by One Straight Line and Formed by Linear Center and Linear System Without Equilibria

Pubblicato online: 01 Jan 2022
Pagine: 47 - 58

Astratto

Abstract

In this paper, we deal with the discontinuous piecewise differential linear systems formed by two differential systems separated by a straight line when one of these two differential systems is a linear without equilibria and the other is a linear center. We are going to show that the maximum number of crossing limit cycles is one, and if exists, it is non algebraic and analytically given.

Parole chiave

  • limit cycle
  • first integral
  • discontinuous piecewise linear differential system
Accesso libero

Controllability of Nonlocal Impulsive Functional Differential Equations with Measure of Noncompactness in Banach Spaces

Pubblicato online: 01 Jan 2022
Pagine: 59 - 80

Astratto

Abstract

This paper is concerned with the controllability of impulsive differential equations with nonlocal conditions. First, we establish a property of measure of noncompactness in the space of piecewise continuous functions. Then, by using this property and Darbo-Sadovskii’s Fixed Point Theorem, we get the controllability of nonlocal impulsive differential equations under compactness conditions, Lipschitz conditions and mixed-type conditions, respectively.

Parole chiave

  • controllability
  • impulsive differential equations
  • nonlocal conditions
  • measure of non compactness
  • fixed point theorem
Accesso libero

Oscillation Tests for Linear Difference Equations with Non-Monotone Arguments

Pubblicato online: 01 Jan 2022
Pagine: 81 - 100

Astratto

Abstract

This paper presents sufficient conditions involving limsup for the oscillation of all solutions of linear difference equations with general deviating argument of the form Δx(n)+p(n)x(τ(n))=0,n0[x(n)q(n)x(σ(n))=0,n],\[\Delta x(n) + p(n)x(\tau (n)) = 0,\,n \in {_0}\quad [\nabla x(n) - q(n)x(\sigma (n)) = 0,\,n \in ],\ , where (p(n))n0 and (q(n))n1 are sequences of nonnegative real numbers and (τ(n))n0,(σ(n))n1\[{(\tau (n))_{n \ge 0}},\quad {(\sigma (n))_{n \ge 1}}\] are (not necessarily monotone) sequences of integers. The results obtained improve all well-known results existing in the literature and an example, numerically solved in MATLAB, illustrating the significance of these results is provided.

Parole chiave

  • non-monotone argument
  • retarded argument
  • advanced argument
  • oscillation
  • Grönwall inequality
Accesso libero

Oscillation Behaviour of Solutions for a Class of a Discrete Nonlinear Fractional-Order Derivatives

Pubblicato online: 01 Jan 2022
Pagine: 101 - 118

Astratto

Abstract

Based on the generalized Riccati transformation technique and some inequality, we study some oscillation behaviour of solutions for a class of a discrete nonlinear fractional-order derivative equation Δ[γ()[α()+β()Δμu()]η]+ϕ()f[G()]=0,N0+1μ, \[\Delta [\gamma (\ell ){[\alpha (\ell ) + \beta (\ell ){\Delta ^\mu }u(\ell )]^\eta }] + \phi (\ell )f[G(\ell )] = 0,\ell \in {N_{{\ell _0} + 1 - \mu }},\] where 0>0,G()=j=01+μ(j1)(μ)u(j)\[{\ell _0} > 0,\quad G(\ell ) = \sum\limits_{j = {\ell _0}}^{\ell - 1 + \mu } {{{(\ell - j - 1)}^{( - \mu )}}u(j)} \] and Δμ is the Riemann-Liouville (R-L) difference operator of the derivative of order μ, 0 < μ ≤ 1 and η is a quotient of odd positive integers. Illustrative examples are given to show the validity of the theoretical results.

Parole chiave

  • oscillation
  • Riemann-Liouville fractional derivatives
  • difference equations
Accesso libero

Oscillatory Behaviour of Second-Order Nonlinear Differential Equations with Mixed Neutral Terms

Pubblicato online: 01 Jan 2022
Pagine: 119 - 134

Astratto

Abstract

The authors examine the oscillation of second-order nonlinear differential equations with mixed nonlinear neutral terms. They present new oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are illustrated by some examples.

Parole chiave

  • oscillation
  • second order
  • neutral differential equations
  • mixed neutral term
Accesso libero

Properties of the Katugampola Fractional Operators

Pubblicato online: 01 Jan 2022
Pagine: 135 - 148

Astratto

Abstract

In this work, there are considered higher order fractional operators defined in the sense of Katugampola. There are proved some fundamental properties of the Katugampola fractional operators of any arbitrary real order. Moreover, there are given conditions ensuring existence of the higher order Katugampola fractional derivative in space of the absolutely continuous functions.

Parole chiave

  • fractional calculus
  • Katugampola fractional operators
  • higher order
  • existence
Accesso libero

Existence of The Asymptotically Periodic Solution to the System of Nonlinear Neutral Difference Equations

Pubblicato online: 01 Jan 2022
Pagine: 149 - 162

Astratto

Abstract

The system of nonlinear neutral difference equations with delays in the form { Δ(yi(n)+pi(n)yi(nτi))=ai(n)fi(yi+1(n))+gi(n),Δ(ym(n)+pm(n)ym(nτm))=am(n)fm(y1(n))+gm(n),\[\left\{ \begin{array}{l} \Delta ({y_i}(n) + {p_i}(n){y_i}(n - {\tau _i})) = {a_i}(n){f_i}({y_{i + 1}}(n)) + {g_i}(n),\\ \Delta ({y_m}(n) + {p_m}(n){y_m}(n - {\tau _m})) = {a_m}(n){f_m}({y_1}(n)) + {g_m}(n), \end{array} \right.\] for i = 1, . . . , m − 1, m ≥ 2, is studied. The sufficient conditions for the existence of an asymptotically periodic solution of the above system, are established. Here sequences (pi(n)), i = 1,..., m, are bounded away from -1. The presented results are illustrated by theoretical and numerical examples.

Parole chiave

  • Difference equation
  • delays
  • neutral type
  • periodicity
  • asymptotic behaviour
Accesso libero

Certain Singular Distributions and Fractals

Pubblicato online: 01 Jan 2022
Pagine: 163 - 198

Astratto

Abstract

In the presented paper, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in their own nega-P-representation. Topological, metric, and fractal properties of images of certain self-similar fractals under the action of some singular distributions, are investigated.

Parole chiave

  • Fractal
  • Moran structure
  • Hausdorff dimension
  • range of values of a function
  • continuous function
Accesso libero

Existence and Multiplicity of Positive Solutions for a Third-Order Two-Point Boundary Value Problem

Pubblicato online: 01 Jan 2022
Pagine: 199 - 212

Astratto

Abstract

We study the existence and multiplicity of positive solutions for a third-order two-point boundary value problem by applying Krasnosel’skii’s fixed point theorem. To illustrate the applicability of the obtained results, we consider some examples.

Parole chiave

  • Nonlinear boundary value problems
  • existence and multiplicity of positive solutions
  • Green’s function
  • Krasnosel’skii’s fixed point theorem
12 Articoli
Accesso libero

Application of the Extended Fan Sub-Equation Method to Time Fractional Burgers-Fisher Equation

Pubblicato online: 01 Jan 2022
Pagine: 1 - 12

Astratto

Abstract

In this paper, the extended Fan sub-equation method to obtain the exact solutions of the generalized time fractional Burgers-Fisher equation is applied. By applying this method, we obtain different solutions that are benefit to further comprise the concepts of complex nonlinear physical phenomena. This method is simple and can be applied to several nonlinear equations. Fractional derivatives are taken in the sense of Jumarie’s modified Riemann-Liouville derivative. A comparative study with the other methods approves the validity and effectiveness of the technique, and on the other hand, for suitable parameter values, we plot 2D and 3D graphics of the exact solutions by using the extended Fan sub-equation method. In this work, we use Mathematica for computations and programming.

Parole chiave

  • extended Fan sub-equation method
  • time fractional Burgers-Fisher equation
  • solitary wave solution
Accesso libero

Some Results Involving the Airy Functions and Airy Transforms

Pubblicato online: 01 Jan 2022
Pagine: 13 - 32

Astratto

Abstract

In the present work, the author studied some properties of the modified Bessel’s functions and Airy functions. It is worth mentioning that the Airy functions are used in many fields of physics. They are applied in many branches of classical and quantum physics. The author also studied certain properties of the Airy transform and derived some new integral relations involving the Airy functions. Non-trivial illustrative examples are provided as well. All the results are presented in lucid and comprehensible language.

Parole chiave

  • Airy function
  • Airy transform
  • modified Bessel functions
  • Riccati differential equation
  • Parseval-Plancherel identity
Accesso libero

Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point

Pubblicato online: 01 Jan 2022
Pagine: 33 - 46

Astratto

Abstract

The problems of existence of limit cycles and their numbers are the most difficult problems in the dynamical planar systems. In this paper, we study the limit cycles for a family of polynomial differential systems of degree 6k + 1, k ∈ ℕ*, with the non-elementary singular point. Under some suitable conditions, we show our system exhibiting two non algebraic or two algebraic limit cycles explicitly given. To illustrate our results we present some examples.

Parole chiave

  • Algebraic and non–algebraic limit cycle
  • planar polynomial differential system
  • first integral
Accesso libero

Explicit Non Algebraic Limit Cycle for a Discontinuous Piecewise Differential Systems Separated by One Straight Line and Formed by Linear Center and Linear System Without Equilibria

Pubblicato online: 01 Jan 2022
Pagine: 47 - 58

Astratto

Abstract

In this paper, we deal with the discontinuous piecewise differential linear systems formed by two differential systems separated by a straight line when one of these two differential systems is a linear without equilibria and the other is a linear center. We are going to show that the maximum number of crossing limit cycles is one, and if exists, it is non algebraic and analytically given.

Parole chiave

  • limit cycle
  • first integral
  • discontinuous piecewise linear differential system
Accesso libero

Controllability of Nonlocal Impulsive Functional Differential Equations with Measure of Noncompactness in Banach Spaces

Pubblicato online: 01 Jan 2022
Pagine: 59 - 80

Astratto

Abstract

This paper is concerned with the controllability of impulsive differential equations with nonlocal conditions. First, we establish a property of measure of noncompactness in the space of piecewise continuous functions. Then, by using this property and Darbo-Sadovskii’s Fixed Point Theorem, we get the controllability of nonlocal impulsive differential equations under compactness conditions, Lipschitz conditions and mixed-type conditions, respectively.

Parole chiave

  • controllability
  • impulsive differential equations
  • nonlocal conditions
  • measure of non compactness
  • fixed point theorem
Accesso libero

Oscillation Tests for Linear Difference Equations with Non-Monotone Arguments

Pubblicato online: 01 Jan 2022
Pagine: 81 - 100

Astratto

Abstract

This paper presents sufficient conditions involving limsup for the oscillation of all solutions of linear difference equations with general deviating argument of the form Δx(n)+p(n)x(τ(n))=0,n0[x(n)q(n)x(σ(n))=0,n],\[\Delta x(n) + p(n)x(\tau (n)) = 0,\,n \in {_0}\quad [\nabla x(n) - q(n)x(\sigma (n)) = 0,\,n \in ],\ , where (p(n))n0 and (q(n))n1 are sequences of nonnegative real numbers and (τ(n))n0,(σ(n))n1\[{(\tau (n))_{n \ge 0}},\quad {(\sigma (n))_{n \ge 1}}\] are (not necessarily monotone) sequences of integers. The results obtained improve all well-known results existing in the literature and an example, numerically solved in MATLAB, illustrating the significance of these results is provided.

Parole chiave

  • non-monotone argument
  • retarded argument
  • advanced argument
  • oscillation
  • Grönwall inequality
Accesso libero

Oscillation Behaviour of Solutions for a Class of a Discrete Nonlinear Fractional-Order Derivatives

Pubblicato online: 01 Jan 2022
Pagine: 101 - 118

Astratto

Abstract

Based on the generalized Riccati transformation technique and some inequality, we study some oscillation behaviour of solutions for a class of a discrete nonlinear fractional-order derivative equation Δ[γ()[α()+β()Δμu()]η]+ϕ()f[G()]=0,N0+1μ, \[\Delta [\gamma (\ell ){[\alpha (\ell ) + \beta (\ell ){\Delta ^\mu }u(\ell )]^\eta }] + \phi (\ell )f[G(\ell )] = 0,\ell \in {N_{{\ell _0} + 1 - \mu }},\] where 0>0,G()=j=01+μ(j1)(μ)u(j)\[{\ell _0} > 0,\quad G(\ell ) = \sum\limits_{j = {\ell _0}}^{\ell - 1 + \mu } {{{(\ell - j - 1)}^{( - \mu )}}u(j)} \] and Δμ is the Riemann-Liouville (R-L) difference operator of the derivative of order μ, 0 < μ ≤ 1 and η is a quotient of odd positive integers. Illustrative examples are given to show the validity of the theoretical results.

Parole chiave

  • oscillation
  • Riemann-Liouville fractional derivatives
  • difference equations
Accesso libero

Oscillatory Behaviour of Second-Order Nonlinear Differential Equations with Mixed Neutral Terms

Pubblicato online: 01 Jan 2022
Pagine: 119 - 134

Astratto

Abstract

The authors examine the oscillation of second-order nonlinear differential equations with mixed nonlinear neutral terms. They present new oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are illustrated by some examples.

Parole chiave

  • oscillation
  • second order
  • neutral differential equations
  • mixed neutral term
Accesso libero

Properties of the Katugampola Fractional Operators

Pubblicato online: 01 Jan 2022
Pagine: 135 - 148

Astratto

Abstract

In this work, there are considered higher order fractional operators defined in the sense of Katugampola. There are proved some fundamental properties of the Katugampola fractional operators of any arbitrary real order. Moreover, there are given conditions ensuring existence of the higher order Katugampola fractional derivative in space of the absolutely continuous functions.

Parole chiave

  • fractional calculus
  • Katugampola fractional operators
  • higher order
  • existence
Accesso libero

Existence of The Asymptotically Periodic Solution to the System of Nonlinear Neutral Difference Equations

Pubblicato online: 01 Jan 2022
Pagine: 149 - 162

Astratto

Abstract

The system of nonlinear neutral difference equations with delays in the form { Δ(yi(n)+pi(n)yi(nτi))=ai(n)fi(yi+1(n))+gi(n),Δ(ym(n)+pm(n)ym(nτm))=am(n)fm(y1(n))+gm(n),\[\left\{ \begin{array}{l} \Delta ({y_i}(n) + {p_i}(n){y_i}(n - {\tau _i})) = {a_i}(n){f_i}({y_{i + 1}}(n)) + {g_i}(n),\\ \Delta ({y_m}(n) + {p_m}(n){y_m}(n - {\tau _m})) = {a_m}(n){f_m}({y_1}(n)) + {g_m}(n), \end{array} \right.\] for i = 1, . . . , m − 1, m ≥ 2, is studied. The sufficient conditions for the existence of an asymptotically periodic solution of the above system, are established. Here sequences (pi(n)), i = 1,..., m, are bounded away from -1. The presented results are illustrated by theoretical and numerical examples.

Parole chiave

  • Difference equation
  • delays
  • neutral type
  • periodicity
  • asymptotic behaviour
Accesso libero

Certain Singular Distributions and Fractals

Pubblicato online: 01 Jan 2022
Pagine: 163 - 198

Astratto

Abstract

In the presented paper, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in their own nega-P-representation. Topological, metric, and fractal properties of images of certain self-similar fractals under the action of some singular distributions, are investigated.

Parole chiave

  • Fractal
  • Moran structure
  • Hausdorff dimension
  • range of values of a function
  • continuous function
Accesso libero

Existence and Multiplicity of Positive Solutions for a Third-Order Two-Point Boundary Value Problem

Pubblicato online: 01 Jan 2022
Pagine: 199 - 212

Astratto

Abstract

We study the existence and multiplicity of positive solutions for a third-order two-point boundary value problem by applying Krasnosel’skii’s fixed point theorem. To illustrate the applicability of the obtained results, we consider some examples.

Parole chiave

  • Nonlinear boundary value problems
  • existence and multiplicity of positive solutions
  • Green’s function
  • Krasnosel’skii’s fixed point theorem

Pianifica la tua conferenza remota con Sciendo