The Explicit Formula for Solution of Anomalous Diffusion Equation in the Multi-Dimensional Space

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