Browsing by Author "Baleanu, D"

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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 shifted Jacobi spectral approximations for solving fractional differential equations
(ELSEVIER SCIENCE INC, 2013) Doha, E. H; Bhrawy, AH; Baleanu, D; Ezz-Eldien, S. S.
In this paper, a new formula of Caputo fractional-order derivatives of shifted Jacobi polynomials of any degree in terms of shifted Jacobi polynomials themselves is proved. We discuss a direct solution technique for linear multi-order fractional differential equations (FDEs) subject to nonhomogeneous initial conditions using a shifted Jacobi tau approximation. A quadrature shifted Jacobi tau (Q-SJT) approximation is introduced for the solution of linear multi-order FDEs with variable coefficients. We also propose a shifted Jacobi collocation technique for solving nonlinear multi-order fractional initial value. problems. The advantages of using the proposed techniques are discussed and we compare them with other existing methods. We investigate some illustrative examples of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. (C) 2013 Elsevier Inc. All rights reserved
A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2015) Bhrawy, A. H.; E. H., Doha; Baleanu, D; Ezz-Eldien, S. S.
In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier. (C) 2014 Elsevier Inc. All rights reserved.