Modified hat functions for constrained fractional optimal control problems with ψ-Caputo derivative

In this paper, a class of constrained fractional optimization problems under a dynamic system involving the $\psi$-Caputo fractional derivative is introduced. A computational method based on the modified hat basis functions is developed to solve these problems. This work is done by obtaining a new operational matrix for the $\psi$-Riemann–Liouville fractional integral of the modified hat functions. The established approach utilizes the modified hat functions to approximate the state and control variables, successfully converting the main problem into a set of algebraic equations. This method provides a systematic and efficient way to obtain numerical solutions for this class of problems. Several test problems are examined to verify the accuracy and applicability of the proposed method.