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.

Keywords

• Extended weighted generalized fractional optimal control problems
• Weak Pontryagin’s maximum principle
• Fractional calculus of variations
• Fractional Euler–Lagrange equation and Hamiltonian approach
• Weighted generalized integration by parts