Generalized Hat Functions for Fractional Delay Optimal Control Problems With ψ‐Caputo Fractional Derivative

• Published in: Mathematical methods in the applied sciences Vol. 48; no. 12; pp. 12139 - 12152
• Main Authors: Karami, S., Heydari, M. H., Baleanu, D., Shasadeghi, M.
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 01.08.2025
• Subjects: delay optimal control problem; Derivatives; Fractional calculus; generalized hat functions; operational matrix of ψ$$ \psi $$‐Riemann–Liouville fractional integral; Optimal control; Optimization; ψ$$ \psi $$‐Caputo fractional derivative
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.11018

ABSTRACT The primary focus of this study is to examine delay optimization problems, subject to a dynamical system that involves ψ$$ \psi $$‐Caputo fractional derivative. The generalized hat functions are applied to develop a computational technique for addressing such problems. To achieve this, a new matrix for the ψ$$ \psi $$‐Riemann–Liouville fractional integral of the generalized hat functions is derived. The proposed approach utilizes the generalized hat functions to approximate the control and state variables, successfully converting the solution of the primary problem into a set of algebraic equations. The established algorithm is a straightforward and effective mathematical technique for numerically solving this family of problems. Finally, several examples are examined to validate the accuracy and applicability of the proposed approach.