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

This paper intends on obtaining the explicit solution of $n$-dimensional\nanomalous diffusion equation in the infinite domain with non-zero initial\ncondition and vanishing condition at infinity. It is shown that this equation\ncan be derived from the parabolic integro-differential equation with memory in\nwhich the kernel is $t^{-\\alpha}E_{1-\\alpha,\n1-\\alpha}(-t^{1-\\alpha}),\\alpha\\in(0, 1),$ where $E_{\\alpha, \\beta}$ is the\nMittag-Liffler function. Based on Laplace and Fourier transforms the properties\nof the Fox H-function and convolution theorem, explicit solution for anomalous\ndiffusion equation is obtained.\n

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