Lie group theory for nonlinear fractional K(m,n) type equation with variable coefficients

TL;DR

This paper applies Lie symmetry analysis to a fractional K(m,n) type equation with variable coefficients, deriving symmetries and reduced equations to understand its solutions in nonlinear dispersion regimes.

Contribution

It introduces a novel application of Lie symmetry analysis to fractional K(m,n) equations with variable coefficients, extending the understanding of their solutions.

Findings

Lie point symmetries identified for the fractional PDE

Reduced fractional differential equations derived

Enhanced understanding of nonlinear fractional dispersive equations

Abstract

We investigated the analytical solution of fractional order K(m,n) type equation with variable coefficient which is an extended type of KdV equations into a genuinely nonlinear dispersion regime. By using the Lie symmetry analysis, we obtain the Lie point symmetries for this type of time-fractional partial differential equations (PDE). Also we present the corresponding reduced fractional differential equations (FDEs) corresponding to the time-fractional K(m,n) type equation.