Lie Symmetries and Third- and Fifth-Order Time-Fractional Polynomial Evolution Equations

Abstract

This paper is concerned with a class of ten time-fractional polynomial evolution equations. The one-parameter Lie point symmetries of these equations are found and the symmetry reductions are provided. These reduced equations are transformed into nonlinear ordinary differential equations, which are challenging to solve by conventional methods. We search for power series solutions and demonstrate the convergence properties of such a solution.

Keywords

• time fractional
• Lie symmetry
• Erdélyi–Kober