Numerical solution of fractional variational and optimal control problems via fractional-order Chelyshkov functions

AIMS Mathematics

article

A. I. Ahmed¹  M. S. Al-Sharif¹  M. S. Salim¹  T. A. Al-Ahmary² 

[1] Department of Mathematics, Faculty of Science, Al-Azhar University;Department of Mathematics, College of Science, King Khalid University

关键词: fractional variational problems;    fractional optimal control problems;    fractional-order Chelyshkov functions;    operational matrix;    Lagrange multiplier method;   

DOI  :  10.3934/math.2022960

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, we present a new numerical method based on the fractional-order Chelyshkov functions (FCHFs) for solving fractional variational problems (FVPs) and fractional optimal control problems (FOCPs). The fractional derivatives are considered in the Caputo sense. The operational matrix of fractional integral for FCHFs, together with the Lagrange multiplier method, are used to reduce the fractional optimization problem into a system of algebraic equations. Some results concerning the approximation errors are discussed and the convergence of the presented method is also demonstrated. The performance of the introduced method is tested through several examples. Some comparisons with recent numerical methods are introduced to show the accuracy and effectiveness of the presented method.

【 授权许可】

CC BY