Houssine Zine, El Mehdi Lotfi, Delfim F. M. Torres, Noura Yousfi
Published 2023-12-12Version 1
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.
Comments: 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]
Journal: Results in Control and Optimization 14 (2024), Art. 100356, 5 pp
Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition --- Application to fractional variational problems
Conservation laws for invariant functionals containing compositions
Higher-order Hahn's quantum variational calculus
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