A new computational technique for the analytic treatment of time-fractional Emden-Fowler equations

This paper presents the study of fractional Emden-Fowler (FEF) equations by utilizing a new adequate procedure, specifically the q-homotopy analysis transform method (q-HATM). The EF equation has got greater significance in both physical and mathematical investigation of capillary and nonlinear dispersive gravity waves. The projected technique is tested by considering four illustrations of the time-fractional EF equations. The q-HATM furnish h, known as an auxiliary parameter, by the support of h we can modulate the various stages of convergence of the series solution. Additionally, to certify the resolution and accurateness of the proposed method we fitted the suitable numerical simulations. The redeem results guarantee that the proposed process is more convincing and scrutinizes the extremely nonlinear issues emerging in the field of science and engineering. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.Y. All rights reserved.

Automated summary

This paper presents a study on fractional Emden-Fowler equations using the q-homotopy analysis transform method, testing the technique with four examples and modulating the convergence stages of series solutions through an auxiliary parameter h. Numerical simulations were used to verify the proposed method's resolution and accuracy, showing its effectiveness in addressing highly nonlinear issues in science and engineering. Copyright © 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.Y. All rights reserved.