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

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.