This paper considers nonlinear fractional mixed Volterra-Fredholm integro-differential equation with a nonlocal initial condition. We propose a fixed-point approach to investigate the existence, uniqueness, and Hyers-Ulam-Rassias stability of solutions. Results of this paper are based on nonstandard assumptions and hypothesis and provide a supplementary result concerning the regularity of solutions. We show and illustrate the wide validity field of our findings by an example of problem with nonlocal neutral pantograph equation, involving functional derivative and -Caputo fractional derivative.

中文翻译：

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具有混合Volterra-Fredholm积分微分方程的非线性分数阶问题：存在性，唯一性，HUR稳定性和解的正则性

本文考虑了具有非局部初始条件的非线性分数阶Volterra-Fredholm积分微分方程。我们提出了一种定点方法来研究解的存在性，唯一性和Hyers-Ulam-Rassias稳定性。本文的结果基于非标准的假设和假设，并提供了有关解的规律性的补充结果。我们发现，并通过与外地中立型比例方程问题的一个例子来说明我们的研究结果的有效性宽领域，涉及功能性衍生物和- Caputo分数衍生物。