Fractional Diffusion based on Riemann-Liouville Fractional Derivatives

R. Hilfer

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arXiv · cond-mat/0006427

Fractional Diffusion based on Riemann-Liouville Fractional Derivatives

R. Hilfer

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Abstract

A fractional diffusion equation based on Riemann-Liouville fractional derivatives is solved exactly. The initial values are given as fractional integrals. The solution is obtained in terms of $H$-functions. It differs from the known solution of fractional diffusion equations based on fractional integrals. The solution of fractional diffusion based on a Riemann-Liouville fractional time derivative does not admit a probabilistic interpretation in contrast with fractional diffusion based on fractional integrals. While the fractional initial value problem is well defined and the solution finite at all times its values for $t\to 0$ are divergent.

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R. Hilfer. 2000-06-27. Fractional Diffusion based on Riemann-Liouville Fractional Derivatives. https://arxiv.org/abs/cond-mat/0006427

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