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

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.(c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

The work proposes 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, validating its effectiveness.