An alternative technique for the symmetry reduction of time‐fractional partial differential equation

Abstract

Based on the Lie symmetry method and taking the generalized time‐fractional Burgers equations involving the Riemann–Liouville derivative for example, we propose a new similarity transformation which converts the time‐fractional Burgers equation into a fractional ordinary differential equation without containing the Erdélyi–Kober fractional differential operator. Such type of reduced equations facilitates us to study the properties as well as construct analytical solutions. Consequently, we obtain an exact solution and a new power series solution of the time‐fractional Burgers equation via the reduced equation.