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

Аннотация

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 −αE1−α,1−α(−t 1−α), α ∈ (0, 1), where Eα,β is the Mittag-Liffler function. Based on Laplace and Fourier transforms the properties of the Fox Hfunction and convolution theorem,explicit solutio.