Cauchy Problem for Fractional Diffusion Equations

Details Cauchy Problem for Fractional Diffusion Equations Cauchy Problem for Fractional Diffusion Equations

2003-10-17

arxiv.org/abs/math/0310271v1

Mathematics

Analysis of PDEs

Scientific paper

We consider an evolution equation with the regularized fractional derivative
of an order $\alpha \in (0,1)$ 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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