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arXiv · 1603.05724

Generalized distributed order diffusion equations with composite time fractional derivative

Trifce Sandev·Zivorad Tomovski·Bojan Crnkovic
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Abstract

In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in Fox $H$-functions. The fractional and second moments are derived by using Mittag-Leffler functions. We observe decelerating anomalous subdiffusion in case of two composite time fractional derivatives. Generalized uniformly distributed order diffusion equation, as a model for strong anomalous behavior, is analyzed by using Tauberian theorem. Some previously obtained results are special cases of those presented in this paper.

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Trifce Sandev, Zivorad Tomovski, Bojan Crnkovic. 2016-03-17. Generalized distributed order diffusion equations with composite time fractional derivative. https://doi.org/10.1016/j.camwa.2016.07.009

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