Efficient Solution for Multi-Delay Fractional Optimal Control Problems Via Cubic B-Splines

Abstract

In this article, we address multi-delay fractional optimal control problems using cubic B-spline functions. First, the properties of cubic B-spline functions are presented, and their operational matrices for derivatives of both ordinary and fractional orders are derived. These matrices are then utilized to transform the original problem into an optimization problem, which is subsequently converted into a system of algebraic equations using Lagrange multipliers. The approximate solution is obtained by solving this algebraic system. Numerical results are provided to demonstrate the validity, effectiveness, and stability of the proposed method.