Asymptotics of fundamental solutions for time fractional equations with convolution kernels

Yuri Kondratiev, Andrey Piatnitski, Elena Zhizhina
2020 Fractional Calculus and Applied Analysis  
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