The current work is devoted to investigate evolution problem of nonlocal Cauchy type under “Mittag–Leffler” type fractional derivative which works as nonsingular and nonlocal kernel. For the considered problem, we establish some appropriate results devoted to the qualitative theory of existence and stability analysis. Upon using Banach and Krasnoselskii’s fixed point theorems, we establish the required analysis. Further stability theory of Ulam’s type is constructed by sing nonlinear analysis. Some interesting examples are provided to support our established results.

中文翻译：

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Mittag-Leffler型分数阶导数下的演化问题研究

当前的工作致力于研究“ Mittag-Leffler”类型分数导数下非局部柯西类型的演化问题，该分数导数作为非奇异和非局部内核。对于所考虑的问题，我们建立了一些关于存在性和稳定性分析的定性理论的适当结果。使用Banach和Krasnoselskii的不动点定理后，我们建立了所需的分析。通过进行非线性分析，进一步构造了Ulam型稳定性理论。提供了一些有趣的示例来支持我们的既定结果。