Supplement a high-dimensional time fractional diffusion equation

Abstract

In this article, we discussed a high-dimensional time fractional diffusion equation which is used to write many nonlinear phenomena in three dimensional space diffusion processes. Under the framework of the Lie group theory, one-parameter Lie transformation group of this considered model based on the have known vector fields, can be constructed. Meanwhile, one-dimensional optimal system through the Ibragimov’s method was also obtained. Further, the high-dimensional time fractional diffusion equation can be reduced into the lower dimensional differential equation with the multiple-parameter Erdélyi-Kober fractional operators. Note that the research can be regarded as a supplement for prior work to this model. The results can furnish us a comprehensive knowledge of a high-dimensional time fractional diffusion equation.

Keywords

• 35B06
• 35Qxx
• 35R03