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arXiv · 2312.10086

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

Houssine Zine·El Mehdi Lotfi·Delfim F. M. Torres·Noura Yousfi
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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.

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Houssine Zine, El Mehdi Lotfi, Delfim F. M. Torres, Noura Yousfi. 2023-12-12. A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems. https://doi.org/10.1016/j.rico.2023.100356

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