Fractional generalised homotopy analysis method for solving nonlinear fractional differential equations

This paper presents a novel hybrid technique which is developed by incorporating the fractional derivatives in the generalised integral transform method. Homotopy analysis method is combined with fractional generalised integral transform method to solve the fractional order nonlinear differential equations. The performance of the proposed method is analysed by solving various categories of nonlinear fractional differential equations like Navier Stokes’s model and Riccatti equations, etc. Unlike the other analytical methods, the hybrid method provides a better way to control the convergence region of the obtained series solution through an auxiliary parameter h. Furthermore, as proposed in this paper, the ‘Fractional Generalised Homotopy Analysis Method’ along with the several examples reveal that this method can be effectively used as a tool for solving various kinds of nonlinear fractional differential equations.