This paper is devoted to studying the long and short time behavior of the solutions to a class of non-local in time subdiffusion equations. To this end, we find sharp estimates of the fundamental solutions in Lebesgue spaces using tools of the theory of Volterra equations. Our results include, as particular cases, the so-called time-fractional and the ultraslow reaction-diffusion equations, which have seen much interest during the last years, mostly due to their applications in the modeling of anomalous diffusion processes.

中文翻译：

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非局部时间细分方程的长时和短时行为

本文致力于研究一类非局部时间细分方程解的长时和短时行为。为此，我们使用 Volterra 方程理论的工具找到了勒贝格空间中基本解的精确估计。作为特殊情况，我们的结果包括所谓的时间分数方程和超慢反应扩散方程，这些方程在过去几年中引起了人们的广泛兴趣，主要是由于它们在反常扩散过程建模中的应用。