Abstract The paper deals with the large time asymptotic of the fundamental solution for a time fractional evolution equation with a convolution type operator. In this equation we use a Caputo time derivative of order α ∈ (0, 1), and assume that the convolution kernel of the spatial operator is symmetric, integrable and shows a super-exponential decay at infinity. Under these assumptions we describe the point-wise asymptotic behavior of the fundamental solution in all space-time regions.

中文翻译：

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带卷积核的时间分数方程基本解的渐近性

摘要 本文研究了具有卷积型算子的时间分数阶演化方程基本解的大时间渐近问题。在这个方程中，我们使用阶 α ∈ (0, 1) 的 Caputo 时间导数，并假设空间算子的卷积核是对称的、可积的，并在无穷远处显示超指数衰减。在这些假设下，我们描述了所有时空区域中基本解的逐点渐近行为。