Exact solutions of a modified fractional diffusion equation in the finite and semi-infinite domains

Gang Guo, Kun Li and Yuhui Wang

Physica A: Statistical Mechanics and its Applications, 2015, vol. 417, issue C, 193-201

Abstract: We investigate the solutions of a modified fractional diffusion equation which has a secondary fractional time derivative acting on a diffusion operator. We obtain analytical solutions for the modified equation in the finite and semi-infinite domains subject to absorbing boundary conditions. Most of the results have been derived by using the Laplace transform, the Fourier Cosine transform, the Mellin transform and the properties of Fox H function. We show that the semi-infinite solution can be expressed using an infinite series of Fox H functions similar to the infinite case, while the finite solution requires double infinite series including both Fox H functions and trigonometric functions instead of one infinite series. The characteristic crossover between more and less anomalous behaviour as well as the effect of absorbing boundary conditions are clearly demonstrated according to the analytical solutions.

Keywords: Modified fractional diffusion equation; Anomalous diffusion; Finite domain; Semi-infinite domain; Fox H function (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:417:y:2015:i:c:p:193-201

DOI: 10.1016/j.physa.2014.09.050

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