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 recently introduced 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 corresponding Euler-Lagrange equations are obtained and one illustrative example is discussed.