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

TL;DR

This paper introduces an efficient numerical method using fractional wavelet operational matrices to solve multi-dimensional fractional optimal control problems, transforming them into algebraic systems for easier computation.

Contribution

The paper develops a novel fractional wavelet operational matrix approach for solving fractional optimal control problems, including convergence and error analysis.

Findings

Method successfully solves illustrative fractional control problems.

Approximate solutions closely match exact solutions.

Convergence rate and error bounds are established.

Abstract

This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine fractional derivatives and integral fractional wavelets, operational matrices were devised and utilised to solve fractional optimal control problems. The proposed method reduced the fractional optimal control problems into a system of algebraic equations. To validate the effectiveness of the presented numerical approach, some illustrative problems were solved using fractional Taylor and Taylor wavelets, and the approximate cost function value derived by approximating state and control functions was compared. In addition, convergence rate and error bound of the proposed method have been derived.