In literature, the integro-differential equations (IDEs) are very much common in the engineering as well in the scientific fields for modeling of dynamical problems. There is a large number of contributions in the study of IDEs for the integer orders. But the cases in fractional order are limited and need consideration of the researchers in the area. In this paper, we initiate a study for fractional Volterra IDEs with Mittag-Leffler kernel for the existence, stability and numerical simulations. For the expression of the results, illustrative work is included.

中文翻译：

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带有 MITTAG-LEFFLER 内核的分数阶 VOLTERRA 积分-微分方程

在文献中，积分微分方程 (IDE) 在工程和科学领域中非常常见，用于对动力学问题进行建模。在整数阶 IDE 的研究中有大量贡献。但是分数顺序的案例是有限的，需要该领域的研究人员考虑。在本文中，我们启动了对具有 Mittag-Leffler 内核的分数 Volterra IDE 的存在性、稳定性和数值模拟的研究。对于结果的表达，包括说明性工作。