Time-fractional inhomogeneous nonlinear diffusion equation: Symmetries, conservation laws, invariant subspaces, and exact solutions

被引：10

作者：

Feng, Wei ^{[1
]}

Zhao, Songlin ^{[1
]}

机构：

[1] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310023, Zhejiang, Peoples R China

来源：

MODERN PHYSICS LETTERS B | 2018年 / 32卷 / 32期

基金：

中国国家自然科学基金;

关键词：

Fractional inhomogeneous nonlinear diffusion equation; conservation laws; invariant subspace; exact solutions; LIE-BACKLUND SYMMETRIES; FORMULATION; THEOREM; ORDER;

D O I：

10.1142/S0217984918504018

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

In this paper, a class of time-fractional inhomogeneous nonlinear diffusion equation (tFINDE) with Riemann-Liouville fractional derivative is studied. All point symmetries admitted by this equation are derived. The optimal system of one-dimensional subal-gebras is classified to perform the symmetry reductions. It is shown that the tFINDE can be reduced to fractional ordinary differential equations (FODEs), including Erdelyi- Kober fractional derivatives. As the results, some explicit group-invariant solutions are obtained. Through nonlinear self-adjointness, all conservation laws admitted by tFINDE arising from these point symmetry groups are listed. The method of invariant subspace is also applied to reduce the tFINDE to a two-dimensional dynamical system (DS). The admitted point symmetries of DS are used to derive the exact solutions of DS, which determine the exact solutions of the original tFINDE.

引用

页数：32

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