Asymptotics of fundamental solutions for time fractional equations with convolution kernels

The paper deals with the large time asymptotic of the fundamental solution for a time fractional evolution equation for a convolution type operator. In this equation we use a Caputo time derivative of order $α$ with $α\in(0,1)$, 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.

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