rss_2.0Moroccan Journal of Pure and Applied Analysis FeedSciendo RSS Feed for Moroccan Journal of Pure and Applied Analysis Journal of Pure and Applied Analysis 's Cover Stable Discontinuous Galerkin Finite Element Method with Multi-Dimensional Slope Limitation for Euler Equations<abstract><title style='display:none'>Abstract</title><p>We present an entropy stable Discontinuous Galerkin (DG) finite element method to approximate systems of 2-dimensional symmetrizable conservation laws on unstructured grids. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. The method is designed to work on structured as well as on unstructured meshes. As solutions of hyperbolic conservation laws can develop discontinuities (shocks) in finite time, we include a multidimensional slope limitation step to suppress spurious oscillations in the vicinity of shocks. The numerical scheme has two steps: the first step is a finite element calculation which includes calculations of fluxes across the edges of the elements using 1-D entropy stable solver. The second step is a procedure of stabilization through a truly multi-dimensional slope limiter. We compared the Entropy Stable Scheme (ESS) versus Roe’s solvers associated with entropy corrections and Osher’s solver. The method is illustrated by computing solution of the two stationary problems: a regular shock reflection problem and a 2-D flow around a double ellipse at high Mach number.</p></abstract>ARTICLE2021-09-30T00:00:00.000+00:00An efficient algorithm for solving the conformable time-space fractional telegraph equations<abstract> <title style='display:none'>Abstract</title> <p>In this paper, an efficient algorithm is proposed for solving one dimensional time-space-fractional telegraph equations. The fractional derivatives are described in the conformable sense. This algorithm is based on shifted Chebyshev polynomials of the fourth kind. The time-space fractional telegraph equations is reduced to a linear system of second order differential equations and the Newmark’s method is applied to solve this system. Finally, some numerical examples are presented to confirm the reliability and effectiveness of this algorithm.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00Some fixed point theorems of rational type contraction in -metric spaces<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we prove some common fixed point theorems satisfying contractive type mapping in the setting of <italic>b</italic>-metric spaces. The presented theorem is an extension the results of M. Sarwar and M. U. Rahman [23] as well as a generalization of many well-known results in the literature through the context of b-metric spaces. Also, we present a few examples to illustrate the validity of the results obtained in the paper. Finally, results are applied to find the solution for an integral equation.</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00Jacobson’s Lemma in the ring of quaternionic linear operators<abstract> <title style='display:none'>Abstract</title> <p>In the present paper, we study the Jacobson’s Lemma in the unital ring of all bounded right linear operators ℬ<italic><sub>R</sub></italic>(<italic>X</italic>) acting on a two-sided quaternionic Banach space <italic>X</italic>. In particular, let <italic>A</italic>, <italic>B</italic> ∈ ℬ<italic><sub>R</sub></italic>(<italic>X</italic>) and let <italic>q</italic> ∈ ℍ \ {0}, we prove that <italic>w</italic>(<italic>AB</italic>) \ {0} = <italic>w</italic>(<italic>BA</italic>) \ {0} where <italic>w</italic> belongs to the spherical spectrum, the spherical approximate point spectrum, the right spherical spectrum, the left spherical spectrum, the spherical point spectrum, the spherical residual spectrum and the spherical continuous spectrum. We also prove that the range of (<italic>AB</italic>)<sup>2</sup> − 2Re(<italic>q</italic>)<italic>AB</italic> + |<italic>q</italic>|<sup>2</sup><italic>I</italic> is closed if and only if (<italic>BA</italic>)<sup>2</sup> − 2Re(<italic>q</italic>)<italic>BA</italic> + |<italic>q</italic>|<sup>2</sup><italic>I</italic> has closed range. Finally, we show that (<italic>AB</italic>)<sup>2</sup> − 2Re(<italic>q</italic>)<italic>AB</italic> + |<italic>q</italic>|<sup>2</sup><italic>I</italic> is Drazin invertible if and only if (<italic>BA</italic>)<sup>2</sup> − 2Re(<italic>q</italic>)<italic>BA</italic> + |<italic>q</italic>|<sup>2</sup><italic>I</italic> is.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00Certain Classes of Analytic Functions Associated With -Analogue of -Valent Cătaş Operator<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we investigate several interesting properties for certain class of analytic functions defined by q-analogue of p-valent Cătaş operator. All our results are sharp.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00On a Class of Caputo Time Fractional Problems with Boundary Integral Conditions<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to work out the solvability of a class of Caputo time fractional problems with boundary integral conditions. A generalized formula of integration is demonstrated and applied to establish the a priori estimate of the solution, then we prove the existence which is based on the range density of the operator associated with the problem.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00Integral geometry on discrete matrices<abstract> <title style='display:none'>Abstract</title> <p>In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00Some results about Lipschitz -Nuclear Operators<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to study the onto isometries of the space of strongly Lipschitz <italic>p</italic>-nuclear operators, introduced by D. Chen and B. Zheng (Nonlinear Anal.,75, 2012). We give some new results about such isometrics and we focus, in particular, on the case <italic>F</italic> = ℓ<sub><italic>p</italic>*</sub>.</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00On the generalized fractional Laplace transform<abstract> <title style='display:none'>Abstract</title> <p>In the present paper a generalization of the Laplace transform is introduced and studied. Its inversion formula is also obtained. As an application, we obtain the generalized fractional Laplace transform of a general class of functions and a product of the Fox’s <italic>H</italic>- function and general class of functions. The results obtained are of general nature and capable of yielding a large number of known or new results as special cases. For illustration, some special cases involving important special functions are mentioned.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00Integral inequalities via harmonically -convexity<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we establish some estimates of the left side of the generalized Gauss-Jacobi quadrature formula for harmonic <italic>h</italic>-preinvex functions involving Euler’s beta and hypergeometric functions. The obtained results are mainly based on the identity given by M. A. Noor, K. I. Noor and S. Iftikhar in [17].</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00Extended convergence of a sixth order scheme for solving equations under –continuity conditions<abstract><title style='display:none'>Abstract</title><p>The applicability of an efficient sixth convergence order scheme is extended for solving Banach space valued equations. In previous works, the seventh derivative has been used not appearing on the scheme. But we use only the first derivative that appears on the scheme. Moreover, bounds on the error distances and results on the uniqueness of the solution are provided (not given in earlier works) based on <italic>ω</italic>–continuity conditions. Numerical examples complete this article.</p></abstract>ARTICLE2021-08-18T00:00:00.000+00:00Pricing American Put Option using RBF-NN: New Simulation of Black-Scholes<abstract><title style='display:none'>Abstract</title><p>The present work proposes an Artificial Neural Network framework for calculating the price and delta hedging of American put option. We consider a sequence of Radial Basis function Neural Network, where each network learns the difference of the price function according to the Gaussian basis function. Based on Black Scholes partial differential equation, we improve the superiority of Artificial Neural Network by comparing the performance and the results achieved used in classic Monte Carlo Least Square simulation with those obtained by Neural networks in one dimension. Thus, numerical result shows that the Artificial Neural Network solver can reduce the computing time significantly as well as the error training.</p></abstract>ARTICLE2021-08-10T00:00:00.000+00:00Nonlinear Random Differential Equations with Sequential Fractional Derivatives<abstract><title style='display:none'>Abstract</title><p>This article deals with a solvability for a problem of random fractional differential equations with <italic>n</italic> sequential derivatives and nonlocal conditions. The existence and uniqueness of solutions for the problem is obtained by using Banach contraction principle. New random data concepts for the considered problem are introduced and some related definitions are given. Also, some results related to the dependance on the introduced data are established for both random and deterministic cases.</p></abstract>ARTICLE2021-08-10T00:00:00.000+00:00Existence result for a fractional differential equation involving a special derivative<abstract><title style='display:none'>Abstract</title><p>In this article, we establish certain sufficient conditions to show the existence of solutions of an initial value problem of fractional-ordinary differential equation in Banach space. Our approach is based on a combination of Mönch fixed point theorem and a suitable measure of non-compactness. Also an example is given to illustrate our approach.</p></abstract>ARTICLE2021-08-10T00:00:00.000+00:00On some results on interpolative Kannan-type and CRR-type contractions.<abstract><title style='display:none'>Abstract</title><p>Recently, Karapinar, Aydi and De Hierro introduced the notions of interpolative Kannan-type contractions and interpolative CRR-type contractions and proved that they possess a fixed point when the space is complete. In this paper, we show that the existence of fixed points for interpolative Kannan-type and CRR-type contractions remains true for a metric space which is not necessarily complete and we give a more precise result concerning the behaviour of Picard sequences of arbitrary initial point. We also study some particular classes of interpolative Kannan-type and CRR-type contractions.</p></abstract>ARTICLE2021-08-10T00:00:00.000+00:00Existence and multiplicity results for a Steklov problem involving ((), ())-Laplacian operator<abstract><title style='display:none'>Abstract</title><p>In this work, we are concerned with a generalized Steklov problem with (<italic>p</italic>(<italic>x</italic>), <italic>q</italic>(<italic>x</italic>))-Laplacian operator. Under some appropriate conditions on the data involved in the elliptic problem, we prove the existence of at least three solutions using Ricceri’s three critical points theorem.</p></abstract>ARTICLE2021-08-10T00:00:00.000+00:00Bu’s theorem in the positive situation<abstract><title style='display:none'>Abstract</title><p>In this paper, we valorize the relationship between positive <italic>p</italic>−summing operators and positive strongly <italic>q</italic>−summing operators using (Contemp. Math. 328, 145 − 149 (2003)).</p></abstract>ARTICLE2021-08-10T00:00:00.000+00:00The ideal of Lipschitz classical -compact operators and its injective hull<abstract><title style='display:none'>Abstract</title><p>We introduce and investigate the injective hull of the strongly Lipschitz classical <italic>p</italic>-compact operator ideal defined between a pointed metric space and a Banach space. As an application we extend some characterizations of the injective hull of the strongly Lipschitz classical <italic>p</italic>-compact from the linear case to the Lipschitz case. Also, we introduce the ideal of Lipschitz unconditionally quasi <italic>p</italic>-nuclear operators between pointed metric spaces and show that it coincides with the Lipschitz injective hull of the ideal of Lipschitz classical <italic>p</italic>-compact operators.</p></abstract>ARTICLE2021-08-10T00:00:00.000+00:00Certain subclasses of Spiral-like univalent functions related with Pascal distribution series<abstract> <title style='display:none'>Abstract</title> <p>The purpose of the present paper is to find the sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations for such subclasses in the open unit disk 𝔻. Further, we consider the properties of integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.</p> </abstract>ARTICLE2021-01-29T00:00:00.000+00:00Limit cycles of discontinuous piecewise linear differential systems formed by centers or Hamiltonian without equilibria separated by irreducible cubics<abstract> <title style='display:none'>Abstract</title> <p>The main goal of this paper is to provide the maximum number of crossing limit cycles of two different families of discontinuous piecewise linear differential systems. More precisely we prove that the systems formed by two regions, where, in one region we define a linear center and in the second region we define a Hamiltonian system without equilibria can exhibit three crossing limit cycles having two or four intersection points with the cubic of separation. After we prove that the systems formed by three regions, where, in two noadjacent regions we define a Hamiltonian system without equilibria, and in the third region we define a center, can exhibit six crossing limit cycles having four and two simultaneously intersection points with the cubic of separation.</p> </abstract>ARTICLE2021-01-29T00:00:00.000+00:00en-us-1