Cauchy Problem for Fractional Diffusion Equations
Samuil D. Eidelman, Anatoly N. Kochubei
Abstract
We consider an evolution equation with the regularized fractional derivative of an order α∈ (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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