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Browsing by Author "Zaky, M. A."

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    Article
    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.
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    Article
    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.
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    Article
    Citation Count: Zaky, M. A...et al. (2018). "Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equation", Advances in Difference Equations.
    Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equation
    (Springer International Publishing AG, 2018) Zaky, M. A.; Baleanu, Dumitru; Alzaidy, J. F.; Hashemizadeh, E.; 56389
    In this paper, we investigate numerical solution of the variable-order fractional Galilei advection-diffusion equation with a nonlinear source term. The suggested method is based on the shifted Legendre collocation procedure and a matrix form representation of variable-order Caputo fractional derivative. The main advantage of the proposed method is investigating a global approximation for the spatial and temporal discretizations. This method reduces the problem to a system of algebraic equations, which is easier to solve. The validity and effectiveness of the method are illustrated by an easy-to-follow example.