Browsing by Author "Khader, M. M."

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Citation Count: Khader, M. M...et al. (2021). "A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives", Applied Numerical Mathematics, Vol. 161, pp. 137-146.
A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives
(2021) Khader, M. M.; Saad, Khaled M.; Hammouch, Zakia; Baleanu, Dumitru; 56389
The purpose of this paper is to investigate the spectral collocation method with help of Chebyshev polynomials. We consider the space fractional Korteweg-de Vries and the space fractional Korteweg-de Vries-Burgers equations based on the Caputo-Fabrizio fractional derivative. The proposed method reduces the models under study to a set of ordinary differential equations and then solves the system via the finite difference method. To the best our knowledge this is the first work which studies the Caputo-Fabrizio space fractional derivative for the proposed equations. The results were validated in the case of the classic differential equations in comparison with the exact solution and the calculation of the absolute error, and in the case of fractional differential equations, the results were verified by calculating the residual error function. In both cases, the results are very accurate and effective. The presented method is easy and accurate, and can be applied to many fractional systems. (c) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
Citation Count: Saad, K. M...et al. (2019). "Numerical solutions of the fractional Fisher's type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods", Chaos, Vol. 29, No. 2.
Numerical solutions of the fractional Fisher's type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods
(Amer Inst Physics, 2019) Saad, K. M.; Khader, M. M.; Gomez-Aguilar, J. F.; Baleanu, Dumitru; 56389
The main objective of this paper is to investigate an accurate numerical method for solving a biological fractional model via Atangana-Baleanu fractional derivative. We focused our attention on linear and nonlinear Fisher's equations. We use the spectral collocation method based on the Chebyshev approximations. This method reduced the nonlinear equations to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them by using the finite difference method. This is the first time that this method is used to solve nonlinear equations in Atangana-Baleanu sense. We present the effectiveness and accuracy of the proposed method by computing the absolute error and the residual error functions. The results show that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.