The explicit formula for solution of anomalous diffusion equation in the multi-dimensional space

2020/09/20 by Durdimurod Durdiev, Durdiev, Durdimurod, Elina Shishkina +3
Mathematics · #68-04 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:68-04

paper · pdf · doi:10.48550/arxiv.2009.10594

arxiv created 2020/09/20 · arxiv updated 2020/09/23

Abstract

This paper intends on obtaining the explicit solution of n-dimensional anomalous diffusion equation in the infinite domain with non-zero initial condition and vanishing condition at infinity. It is shown that this equation can be derived from the parabolic integro-differential equation with memory in which the kernel is t^-αE_{1-α, 1-α}(-t^1-α),α∈(0, 1), where E_{α, β} is the Mittag-Liffler function. Based on Laplace and Fourier transforms the properties of the Fox H-function and convolution theorem, explicit solution for anomalous diffusion equation is obtained.

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