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Numerical simulation and convergence analysis of fractional optimization problems with right-sided Caputo fractional derivative

[+] Author and Article Information
Samer Ezz-Eldien

Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, El-Kharja, Egypt
s_sezeldien@yahoo.com

Ahmed El-Kalaawy

Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
ah.elkelaawy@yahoo.co.uk

1Corresponding author.

ASME doi:10.1115/1.4037597 History: Received April 02, 2017; Revised July 10, 2017

Abstract

This paper presents an efficient approximation scheme for the numerical solution of a fractional variational problem (FVP) and fractional optimal control problem (FOCP). As basis function for the trial solution, we employ the shifted Jacobi orthonormal polynomial. We state and derive a new operational matrix of right-sided Caputo fractional derivative of such polynomial. The new methodology of the present scheme is based on the derived operational matrix with the help of the Gauss-Lobatto quadrature formula and the Lagrange multiplier technique. Accordingly, the aforementioned problems are reduced into systems of algebraic equations. The error bound for the operational matrix of right-sided Caputo derivative is analyzed. In addition, the convergence of the proposed approach is also included. The results obtained through numerical procedure and comparing our method with other methods demonstrate the high accuracy and powerful of the present approach.

Copyright (c) 2017 by ASME
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