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

被引：29

作者：

Zheng, Bailin ^{[1
]}

Kai, Yue ^{[1
]}

Xu, Wenlong ^{[1
]}

Yang, Nan ^{[1
]}

Zhang, Kai ^{[1
]}

Thibado, P. M. ^{[2
]}

机构：

[1] Tongji Univ, Sch Aerosp Engn & Appl Mech, Shanghai 200092, Peoples R China

[2] Univ Arkansas, Dept Phys, Fayetteville, AR 72701 USA

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2019年 / 532卷

基金：

中国国家自然科学基金;

关键词：

Conformal fractional derivative; Canonical-like transformation method; Complete discrimination system for polynomial; Anomalous diffusion; RENORMALIZATION METHOD; CLASSIFICATION; COUNTEREXAMPLES;

D O I：

10.1016/j.physa.2019.121780

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：11

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