Symmetries and exact solution of certain nonlinear fractional ordinary differential equations

In this article, we consider a certain class of nonlinear fractional ordinary differential equations, investigate their symmetries and obtain exact solutions wherever possible. In our investigation, we have identified fractional differential equations that admit power type exact solutions and also fractional differential equations that admit exponential type exact solutions. In particular, invariant solutions are found for fractional Abel's differential equation of the first and second kind, fractional Riccati equation and two-coupled system of fractional Riccati equation, with variable coefficients. The results of the analytical investigation reveal that symmetries can be found and used effectively to obtain exact solutions for a wider class of fractional ordinary differential equations.