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.
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Kondratiev, Y., Piatnitski, A. & Zhizhina, E. Asymptotics of Fundamental Solutions for Time Fractional Equations with Convolution Kernels. Fract Calc Appl Anal 23, 1161–1187 (2020). https://doi.org/10.1515/fca-2020-0059
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DOI: https://doi.org/10.1515/fca-2020-0059