Cubic B-spline Approach for Solving Fractional Optimal Control Problems in the Caputo-Fabrizio Sense

Abstract

In this paper, a numerical method is presented for solving fractional optimal control problems (FOCPs) in the Caputo-Fabrizio sense using cubic B-spline functions. Operational matrices for ordinary and fractional derivatives are constructed to facilitate the transformation of the FOCP into a nonlinear programming problem. The Lagrange multiplier method is applied to obtain the optimal solution. Additionally, the error bounds for the proposed approximations are derived to ensure the reliability of the method. The efficiency and accuracy of the approach are demonstrated through three numerical examples, confirming its effectiveness in solving fractional control problems.