In this paper, we consider the initial boundary value problem for time-fractional subdiffusive equations with Caputo derivative. Our problem has many applications in population dynamics. The source function is given in the logarithmic form. We examine the existence, uniqueness of local solutions, and their ability to continue to a maximal interval of existence. The main tool and analysis here are of applying some Sobolev embedding and some fixed point theorems.

中文翻译：

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一类具有对数非线性的半线性非经典分数阶波动方程

在本文中，我们考虑了具有 Caputo 导数的时间分数次扩散方程的初始边值问题。我们的问题在人口动态中有很多应用。源函数以对数形式给出。我们检查了局部解的存在性、唯一性，以及它们在存在的最大间隔上持续的能力。这里的主要工具和分析是应用一些 Sobolev 嵌入和一些不动点定理。