Symmetry reductions and qualitative analysis of time fractional K(m,1) equation

Abstract

This paper studies symmetry reductions of time fractional K(m,1) equation with generalized evolution which is one of the important equation in fractional partial differential equations (FPDEs). Here, the classical Lie symmetries are obtained and utilized for the reduction of time fractional K(m,1) equation into ordinary differential equations. Some new exact solutions are obtained which are in the form of solitary waves by using G′G-expansion method and one of the obtained solutions is acceptable for qualitative analysis. By showing the phase portraits, its dynamical behaviour is further completely explained.

Keywords

• Fractional partial differential equation
• Symmetry analysis
• Bifurcation
• Travelling wave solution