Lie symmetry analysis and exact solution of certain fractional ordinary differential equations

Abstract

A systematic investigation of finding Lie point symmetries of certain fractional linear and nonlinear ordinary differential equations is presented. More precisely, Lie point symmetries of fractional Riccati equation, nonhomogeneous fractional linear ordinary differential equation with variable coefficients and quadratic fractional Lienard-type equation in the sense of Riemann–Liouville fractional derivative are derived. Using the obtained Lie point symmetries, we derive exact solution of the above-mentioned fractional ordinary differential equations wherever possible.