Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations

TL;DR

This paper introduces variable order Mittag-Leffler fractional operators on isolated time scales, providing new tools for fractional calculus and variational problems with variable-order difference operators.

Contribution

It develops a general framework for fractional operators with Mittag-Leffler kernels on isolated time scales and derives related integration by parts and optimality conditions.

Findings

Derived fractional integration by parts formulas

Established necessary conditions for fractional variational problems

Extended fractional calculus to variable order on isolated time scales

Abstract

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main results give fractional integration by parts formulas and necessary optimality conditions of Euler-Lagrange type.