Lie symmetry analysis of time fractional Burgers equation with time-dependent coefficients

Abstract

In this paper, Lie symmetry analysis is applied to study time fractional Burgers equation with time dependent coefficients. Some Lie symmetries for the equation with some kinds of coefficients f(t) and g(t) are obtained. They are used to reduce the aimed equation with Riemann-Liouville fractional derivative to the fractional ordinary equation with Erdélyi-Kober fractional derivative. Then the power series method is applied to derive explicit power series solution for the reduced equation. For the power series solution, we not only provide a proof of its convergence but also conduct numerical simulations and analysis. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equation studied.