Browsing by Author "Amin, Ahmed Z. M."

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Citation - WoS: 15
Citation - Scopus: 14
A Spectral Technique for Solving Two-Dimensional Fractional Integral Equations With Weakly Singular Kernel
(Hacettepe Univ, Fac Sci, 2018) Bhrawy, Ali H.; Baleanu, Dumitru; Abdelkawy, Mohamed A.; Baleanu, Dumitru; Amin, Ahmed Z. M.; 56389; Matematik
This paper adapts a new numerical technique for solving twodimensional fractional integral equations with weakly singular. Using the spectral collocation method, the fractional operators of Legendre and Chebyshev polynomials, and Gauss-quadrature formula, we achieve a reduction of given problems into those of a system of algebraic equations. We apply the reported numerical method to solve several numerical examples in order to test the accuracy and validity. Thus, the novel algorithm is more responsible for solving two-dimensional fractional integral equations with weakly singular.
Citation - WoS: 15
Citation - Scopus: 18
Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations
(inst Mathematics & informatics, 2019) Doha, Eid H.; Baleanu, Dumitru; Abdelkawy, Mohamed A.; Amin, Ahmed Z. M.; Baleanu, Dumitru; 56389; Matematik
In this manuscript, we introduce a spectral technique for approximating the variable-order fractional Riccati differential equation (VOFRDE). Firstly, the solution and its space fractional derivatives is expanded as shifted Chebyshev polynomials series. Then we determine the expansion coefficients by reducing the VOFRDEs and its conditions to a system of algebraic equations. We show the accuracy and applicability of our numerical approach through four numerical examples.
Citation - WoS: 21
Citation - Scopus: 21
Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations
(inst Mathematics & informatics, 2019) Doha, Eid H.; Baleanu, Dumitru; Abdelkawy, Mohamed A.; Amin, Ahmed Z. M.; Baleanu, Dumitru; 56389; Matematik
This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple and very accurate. Furthermore, an error analysis is performed to verify the correctness and feasibility of the proposed method when solving IDE.