Group Classification, Exact Solutions and Conservation Laws of (2+1)-dimensional Time Fractional Konopelchenko-Dubrovsky Equations

In this paper, Lie symmetry analysis method is applied to the (2 + 1)-dimensional time fractional Konopelchenko-Dubrovsky equations, which is an important model in physics. We obtained and classified all the Lie symmetries admitted by the equations according to the coefficients. Then we used the obtained group classification to reduce the (2 + 1)-dimensional fractional partial differential equations with Riemann-Liouville fractional derivative to some (1 + 1)-dimensional fractional partial differential equations with Erédlyi-Kober fractional derivative, thereby getting some exact solutions of the reduced equations. In addition, the new conservation theorem and the generalisation of Noether operators are developed to construct the conservation laws for the equations studied.