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Cauchy Problem for Fractional Diffusion Equations

Samuil D. Eidelman·Anatoly N. Kochubei
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Abstract

We consider an evolution equation with the regularized fractional derivative of an order $α\in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables. Such equations describe diffusion on inhomogeneous fractals. A fundamental solution of the Cauchy problem is constructed and investigated.

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Samuil D. Eidelman, Anatoly N. Kochubei. 2012-06-24. Cauchy Problem for Fractional Diffusion Equations. https://arxiv.org/abs/math/0310271

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