Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel

Abstract

In this manuscript we define the right fractional derivative and its corresponding right fractional integral for the newly suggested nonlocal fractional derivative with Mittag-Leffler kernel. Then, we obtain the related integration by parts formula. We use the Q-operator to confirm our results. The related Euler-Lagrange equations are reported and one illustrative example is discussed.