The conservation laws with Lie symmetry analysis for time fractional integrable coupled KdV-mKdV system

In this paper, the fractional Lie symmetry method has been implemented for getting similarity reduction and conservation laws for time fractional integrable coupled KdV-mKdV system. Firstly, the fractional Lie symmetry method has been used for getting the infinitesimal generators for the time fractional integrable coupled KdV-mKdV system. Then, by using of Erdélyi-Kober differential operators via Riemann-Liouville derivative, the reduction of coupled fractional differential equations to coupled fractional ordinary differential equations has been presented. Also, by means of new conservation theorem with formal Lagrangian, the new conserved vectors have been derived for the time fractional integrable coupled KdV-mKdV system.