Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels

Abstract

Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall type inequality as well as results on continuity and differentiability of perturbed trajectories. Moreover, a Mangasarian type sufficient global optimality condition for the general analytic kernel fractional optimal control problem is proved. An illustrative example is discussed.

Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems

“…Also, it enriches the subject of Pontryagin's maximum principle to handle a more general and wide class of fractional-order operators. For instance, a maximum principle is obtained for a combined fractional operator with a general analytic kernel in [20]. Also, some recent results for the Pontryagin maximum principle are investigated for fractional stochastic delayed systems with non-instantaneous impulses [21], for a degenerate fractional differential equation [22], and for distributed-order fractional derivatives [23].…”