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

2016/06/25 by Thabet Abdeljawad, Dumitru Baleanu, Dumitru Bǎleanu +2
Mathematics · #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Nonlinear Differential Equations Analysis #math.CA

paper · pdf · doi:10.48550/arxiv.1607.00262

arxiv created 2016/06/25 · arxiv updated 2016/07/04

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.

Related

• New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
• Fractional Differential Equations Involving Caputo Fractional Derivative with Mittag-Leffler Non-Singular Kernel: Comparison Principles and Applications
• On the local M-derivative
• Mittag-Leffler functions and the truncated V-fractional derivative
• Properties of fractional integral operators involving the three-parameters Mittag-Leffler function in the kernels with respect to another function