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 \(t^{-\alpha}E_{1-\alpha,1-\alpha}(-t^{1-\alpha})\), \(\alpha\in(0,1),\) where \(E_{\alpha,\beta}\) 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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Durdiev, D., Shishkina, E. & Sitnik, S. The Explicit Formula for Solution of Anomalous Diffusion Equation in the Multi-Dimensional Space. Lobachevskii J Math 42, 1264–1273 (2021). https://doi.org/10.1134/S199508022106007X
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DOI: https://doi.org/10.1134/S199508022106007X