A Numerical Approach for Fractional Optimal Control Problems by Using Ritz Approximation

Document Type : Special issue editorial

Authors
A. Ramezanpour 1
P. Reihani 1
J. Vahidi 2
F. Soltanian 1
1 Department of Mathematics, Payame Noor University, Tehran, Iran
2 Department of Mathematics, Iran University of science and Technology, Tehran,Iran. Department of Mathematical Sciences, University of South Africa, UNISA0003,South Africa
10.22075/ijnaa.2019.4397
Abstract
In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the numerical solution is investigated. Some numerical examples are presented which illustrate the theoretical results and the performance of the method.
Keywords
Fractional Optimal Control Problems
Caputo fractional derivative
Optimal Control Problems
Polynomial basis functions

  • Receive Date 02 May 2019
  • Revise Date 16 October 2019
  • Accept Date 08 November 2019

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