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AbstractThe 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.doi:10.1515/fca-2020-0059 fatcat:zpyzpghjtnctpod6w33k7abmdi