A novel hybrid technique to obtain the solution of generalized fractional-order differential equations

Abstract

The motive of the work is to propose a new hybrid technique, the Homotopy Perturbation General Transform Method (HPGTM) for obtaining an analytic solution for a wide class of time-fractional differential equations in the Caputo sense. The efficiency of HPGTM is analyzed using a comparative study with Adomian Decomposition Method (ADM), Residual Power Series Method (RPSM), and exact solution. Numerical examples including well-known equations viz. radioactive decay model, Riccati equation, backward Kolmogorov equation, Klein–Gordon equation, and Rosenau–Hyman equation are considered in arbitrary order. The outcomes of numerical simulations clearly state the effectiveness of the present method.