LIE SYMMETRY, EXACT SOLUTIONS AND CONSERVATION LAWS OF SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

In this paper, Lie symmetry analysis method is applied to space-time fractional reaction-diffusion equations and diffusion-convection Boussi-nesq equations. The Lie symmetries for the governing equations are obtained and used to get group generators for reducing the space-time fractional partial differential equations(FPDEs) with Riemann-Liouville fractional derivative to space-time fractional ordinary differential equations(FODEs) with Erdelyi-Kober fractional derivative. Then the Laplace transformation and the power series methods are applied to derive explicit solutions for the reduced equa-tions. Moreover, the conservation theorems and the generalization of the Noether operators are developed to acquire the conservation laws for the equa-tions. Some figures for the obtained explicit solutions are also presented.