Solution of Nonlinear Fractional Quadratic Riccati Differential Equations Using Perturbation Method

Abstract

Homotopy perturbation transform method (HPSTM) in conjunction of Adomian and He’s polynomials has been devoted to obtain approximate solution of fractional order quadratic Riccati equations for arbitrary order $$ \alpha \in (0,1] $$. The suggested method finds the solution without any discontinuation and averts the round-off errors. We have taken three examples to justify the accuracy of the method with the help of Adomian polynomials based on Newton–Raphson’s scheme. The approximate solutions are compared with exact solutions.