Group analysis and exact solutions of the time fractional Fokker–Planck equation

• Nonlinear time fractional Fokker–Planck is considered.
• Symmetries and two vector fields of fractional Fokker–Planck equation are extracted.
• Similarity variables are constructed and Erdélyi–Kober operator is utilized for the reduction.
• Reduction method introduced by M.C. Nucci is applied for extracted second order ODE.

In this paper, the Lie symmetry analysis method is extended to deal with the nonlinear time fractional Fokker–Planck (FP) equation with Riemann–Liouville derivative. The Erdélyi–Kober fractional derivative which is depending on a parameter αα, is used for the reduction of FP equation. Symmetry reduction is provided and some exact analytic solutions to the time fractional FP equation are investigated by virtue of the reduction method introduced by M.C. Nucci.