A numerical technique for solving multi-dimensional fractional optimal control problems

Abstract

In this article, we use the operation matrix (OM) of Riemann–Liouville fractional integral of the shifted Gegenbauer polynomials with the Lagrange multiplier method to provide efficient numerical solutions to the multi-dimensional fractional optimal control problems. The proposed technique transforms the under consideration problems into sets of nonlinear equations which are easy to solve. Numerical tests including numerical comparisons with some existing methods are introduced to demonstrate the accuracy and efficiency of the suggested technique.

Keywords

• Riemann–Liouville fractional integral operator
• fractional optimal control problems
• operational matrix
• shifted Gegenbauer polynomials
• Lagrange multiplier method