In this work, we study the existence of mild and classical solutions for neutral partial functional integro-differential equations with non-local condition. We discuss the problems by making full use of resolvent operators theory newly established in the literature, theory of fractional power, \(\alpha \)-norm and Schauder’s fixed point theorem. Some results on existence and regularity of solutions of the considered equation are obtained. Finally, an example is presented to illustrate the obtained results.

中文翻译：

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具有非局部条件的中立型积分微分方程解的存在性和正则性

在这项工作中，我们研究了具有非局部条件的中立型偏泛函积分微分方程的温和经典解的存在。我们通过充分利用文献中新建立的分解算子理论，分数幂理论，\（\ alpha \）-范数和Schauder不动点定理来讨论这些问题。获得了所考虑方程解的存在性和正则性的一些结果。最后，给出一个例子来说明所获得的结果。