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

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A Computationally Efficient Method For a Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions
(Editura Academiei Romane, 2018) El-Kalaawy, Ahmed A.; Doha, Eid H.; Ezz-Eldien, Samer S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Baleanu, Dumitru; Zaky, M. A.; 56389
This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.
Citation Count: Bhrawy, Ali H...et al. (2018). "A spectral technique for solving two-dimensional fractional integral equations with weakly singular kernel", Hacettepe Journal of Mathematics and Statistics, Vol. 47, No. 3, pp, 553-566.
A Spectral Technique for Solving Two-Dimensional Fractional Integral Equations With Weakly Singular Kernel
(Hacettepe Univ, Fac Sci, 2018) Bhrawy, Ali H.; Abdelkawy, M. A.; Baleanu, Dumitru; Amin, A. Z. M.; 56389
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 Count: Doha, E. H...et.al. (2017). "Composite Bernoulli-Laguerre collocation method for a class of hyperbolic telegraph-type equations", Romanian Reports In Physics, Vol.69, No.4.
Composite Bernoulli-Laguerre collocation method for a class of hyperbolic telegraph-type equations
(Editura Academiei Romane, 2017) Doha, E. H.; Hafez, R. M.; Abdelkawy, M. A.; Ezz-Eldien, S. S.; Taha, T. M.; Zaky, M. A.; Amin, A. Z. M.; El-Kalaawy, A. A.; Baleanu, Dumitru; 56389
In this work, we introduce an efficient Bernoulli-Laguerre collocation method for solving a class of hyperbolic telegraph-type equations in one dimension. Bernoulli and Laguerre polynomials and their properties are utilized to reduce the aforementioned problems to systems of algebraic equations. The proposed collocation method, both in spatial and temporal discretizations, is successfully developed to handle the two-dimensional case. In order to highlight the effectiveness of our approachs, several numerical examples are given. The approximation techniques and results developed in this paper are appropriate for many other problems on multiple-dimensional domains, which are not of standard types.
Citation Count: Doha, Eid H...et al. (2019). "Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations", Nonlinear Analysis-Modelling and Control, Vol. 24, No. 3, pp. 332-352.
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.; Abdelkawy, M. A.; Amin, A. Z. M.; Baleanu, Dumitru; 56389
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.
Citation Count: Doha, E. H. (2018). "Spectral technique for solving variable-order fractional Volterra integro-differential equations" Vol.34, No.5, pp. 1659-1677.
Spectral Technique for Solving Variable-Order Fractional Volterra Integro-Differential Equations
(Wiley, 2018) Doha, E. H.; Abdelkawy, M. A.; Amin, A. Z. M.; Baleanu, Dumitru; 56389
This article, presented a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method which is introduced for solving variable-order fractional Volterra integro-differential equation (VO-FVIDEs) subject to initial or nonlocal conditions. Based on shifted Legendre Gauss-Lobatto (SL-GL) quadrature, we treat with integral term in the aforementioned problems. Via the current approach, we convert such problem into a system of algebraic equations. After that we obtain the spectral solution directly for the proposed problem. The high accuracy of the method was proved by several illustrative examples.
Citation Count: Doha, E. H...et al. (2018). "Spectral technique for solving variable-order fractional Volterra integro-differential equations", Numerical Methods for Partial Differential Equations, Vol. 34, No. 5, pp. 1659-1677.
Spectral technique for solving variable-order fractional Volterra integro-differential equations
(Wiley, 2018) Doha, E. H.; Abdelkawy, M. A.; Amin, A. Z. M.; Baleanu, Dumitru; 56389
This article, presented a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method which is introduced for solving variable-order fractional Volterra integro-differential equation (VO-FVIDEs) subject to initial or nonlocal conditions. Based on shifted Legendre Gauss-Lobatto (SL-GL) quadrature, we treat with integral term in the aforementioned problems. Via the current approach, we convert such problem into a system of algebraic equations. After that we obtain the spectral solution directly for the proposed problem. The high accuracy of the method was proved by several illustrative examples.