标题： 分部积分及其在具有 Mittag-Leffler 非奇异核的新非局部分数阶导数中的应用 显示英文标题

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

摘要： 在本文中，我们定义了最近引入的具有Mittag-Leffler核的非局部分数阶导数的右分数阶导数及其相应的右分数阶积分。 然后，我们得到了相关的分部积分公式。 我们使用$Q-$算子来验证我们的结果。 得到了相应的欧拉-拉格朗日方程，并讨论了一个示例。 显示英文摘要

摘要： 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.