On Mittag-Leffler Kernel-Dependent Fractional Operators With Variable Order

Abstract

In this work, integration by parts formulas for variable-order fractional operators with Mittag-Leffler kernels are presented and applied to study constrained fractional variational principles involving variable-order Caputo-type Atangana–Baleanu’s derivatives, where the variable-order fractional Euler–Lagrange equations are investigated. A general formulation of fractional Optimal Control Problems (FOCPs) and a solution scheme for such class of systems are proposed. The performance index of a FOCP is taken into consideration as function of state as well as control variables. © 2019, Springer Nature Singapore Pte Ltd.