Browsing by Author "Abdelkawy, M. A"

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AN ACCURATE NUMERICAL TECHNIQUE FOR SOLVING FRACTIONAL OPTIMAL CONTROL PROBLEMS
(EDITURA ACAD ROMANE, 2015-03) Abdelkawy, M. A; Ezz-Eldien, S. S; Baleanu, D; Doha, E. H; Bhrawy, A. H
In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.
COMPOSITE BERNOULLI-LAGUERRE COLLOCATION METHOD FOR A CLASS OF HYPERBOLIC TELEGRAPH-TYPE EQUATIONS
(EDITURA ACAD ROMANE, 2017) Baleanu, D; El-Kalaawy, A. A; Amin, A. Z. M; Zaky, M. A; Taha, T. M; Ezz-Eldien, S. S; Abdelkawy, M. A; Hafez, R. M.; Doha, E. H
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.
On Numerical Methods for Fractional Differential Equation on a Semi-infinite Interval
(DE GRUYTER OPEN LTD, 2015) Hafez, R. M.; Abdelkawy, M. A; Taha, T. M; Bhrawy, A. H
Chapter 11 is devoted to numerical solutions of fractional differential equations (FDEs) on a semi-infinite interval. This chapter presents a broad discussion of spectral techniques based on operational matrices of fractional derivatives and integration methods for solving several kinds of linear and nonlinear FDEs. We present the operational matrices of fractional derivatives and integrals for some orthogonal polynomials/functions on a semi-infinite interval, and use them together with different spectral techniques for solving the aforementioned equations on a semi-infinite interval. Numerous examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on a semi-infinite interval.