Lie symmetries, symmetry reductions and conservation laws of time fractional modified Korteweg-de Vries (mkdv) equation

In this work, we study Lie symmetry analysis for fractional order differential equations that is one of the applications of symmetries. This study deals with Lie symmetry of fractional order modified Korteweg-de Vries (mKdV) equation. We found Lie symmetries of this equation and then we reduced fractional order modified Korteweg-de Vries (mKdV) equation to fractional order ordinary differential equation with Erdelyi-Kober fractional differential operator. Then we used characteristic method for fractional order differential equations and help of founded these Lie symmetries for finding solutions for given equation. Then we obtained infinite and finite conservation laws of fractional order modified Korteweg-de Vries (mKdV) equation.