The aim of this paper is to investigate the existence of mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition. Unlike previous papers, in the current paper, we assume that the source function of the problem may have a singularity. The existence results are proven via the Schaefer, nonlinear Leray–Schauder alternatives and Banach fixed point theorems. Further, the continuity of mild solutions in terms of inputs (fractional orders, nonlocal condition, and associated parameters) is extensively discussed.

中文翻译：

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非局部条件下广义非线性分数阶拟抛物方程的温和解

本文的目的是研究具有非局部条件的广义非线性分数阶拟抛物方程的温和解的存在性。与之前的论文不同，在当前论文中，我们假设问题的源函数可能具有奇异性。存在性结果通过 Schaefer、非线性 Leray-Schauder 替代方案和 Banach 不动点定理证明。此外，广泛讨论了输入（分数阶、非局部条件和相关参数）方面的温和解的连续性。