Exact traveling and non-traveling wave solutions of the time fractional reaction–diffusion equation

Bailin Zheng, Yue Kai, Wenlong Xu, Nan Yang, Kai Zhang and P.M. Thibado

Physica A: Statistical Mechanics and its Applications, 2019, vol. 532, issue C

Abstract: In this study, solutions to the nonlinear time-dependent fractional reaction–diffusion equation with conformal fractional derivative is considered. In the first part of the manuscript, we reduce the fractional equation to a traditional differential equation using the fractional complex transformation. Two cases where the exact solution exists are then presented. One of these solutions is used to model experimental data showing anomalous diffusion in freestanding graphene. In the second part, we study the traveling solutions and present two cases: Canonical-like transformation method and complete discrimination system for polynomial method.

Keywords: Conformal fractional derivative; Canonical-like transformation method; Complete discrimination system for polynomial; Anomalous diffusion (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119310349

DOI: 10.1016/j.physa.2019.121780

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