A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems

Abstract

Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of Pontryagin's maximum principle is proved. As corollaries, necessary optimality conditions for Caputo-Fabrizio, Atangana-Baleanu and weighted Atangana-Baleanu fractional dynamic optimization problems are trivially obtained. As an application, the weighted generalized fractional problem of the calculus of variations is investigated and a new more general fractional Euler-Lagrange equation is given.

This is a preprint version of the paper published open access in 'Results in Control and Optimization 14 (2024), Art. 100356, 5 pp' [https://doi.org/10.1016/j.rico.2023.100356]

References in corpus (5)

• Fractional Noether's theorem in the Riesz-Caputo sense
• A Stochastic Fractional Calculus with Applications to Variational Principles
• Pontryagin Maximum Principle for Distributed-Order Fractional Systems
• Weighted Generalized Fractional Integration by Parts and the Euler-Lagrange Equation
• Weak Pontryagin's Maximum Principle for Optimal Control Problems Involving a General Analytic Kernel