Lie symmetry analysis and conservation laws of certain time fractional partial differential equations

Abstract

A method is presented to derive the Lie point symmetries of time fractional partial differential equations in the sense of Riemann-Liouville fractional derivative. The applicability of the method has been illustrated through time fractional Burgers-Korteweg-de Vries with time dependent variable coefficients, time fractional dissipative Zabolotskaya-Khokhlov equation, time fractional generalised Benjamin equation and time fractional diffusion equation with variable coefficients. Using the obtained Lie point symmetries, it is shown that each of the above mentioned time fractional partial differential equations can be transformed into a ordinary differential equations of fractional order. Exact solutions of the above mentioned time fractional equations are derived wherever possible. It is also explained how conservation laws can be derived to time fractional partial differential equations.