In this paper, we study a nonlinear ψ−Hilfer fractional integro-differential equation on finite interval $[a,b]$. Sufficient conditions for the existence of solution and stability for the initial value problem are obtained. Firstly, the existence of solution for the equation is proved by using Banach contraction mapping principle. Then the Ulam-Hyers-Rassias stability, Ulam-Hyers stability, Semi-Ulam-Hyers-Rassias stability of the system are discussed.

中文翻译：

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非线性分数阶微分方程解的存在性和稳定性

本文研究有限区间上的非线性ψ -Hilfer分数阶积分-微分方程$[\mathrm{一种}，b]$。获得了存在解的充分条件和初值问题的稳定性。首先，利用Banach压缩映射原理证明了该方程解的存在性。然后讨论了系统的Ulam-Hyers-Rassias稳定性，Ulam-Hyers稳定性，Semi-Ulam-Hyers-Rassias稳定性。