Abstract

In this study, integro-differential equations of arbitrary order are studied. The fractional order is expressed in terms of the \(\psi\)-Hilfer type proportional fractional operator. This research exposes the dynamical behavior of integro-differential equations with fractional order, such as existence, uniqueness, and stability solutions. The initial value problem and nonlocal conditions are used to prove the results.

中文翻译：

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广义比例分数阶导数积分微分方程的存在性和稳定性

摘要

在本研究中，研究了任意阶的积分微分方程。分数阶以\(\psi\) -Hilfer 类型比例分数运算符表示。这项研究揭示了分数阶积分微分方程的动力学行为，例如解的存在性、唯一性和稳定性。初值问题和非局部条件被用来证明结果。