Prospective Analysis of Time-Fractional Emden–Fowler Model Using Elzaki Transform Homotopy Perturbation Method

Abstract

The present study presents a combination of two famous analytical techniques for the analytical solutions of linear and nonlinear time-fractional Emden–Fowler models. We combine the Elzaki transform (ET) and the homotopy perturbation method (HPM) for the development of the Elzaki transform homotopy perturbation method (ET-HPM). In this paper, we demonstrate that the Elzaki transform (ET) simplifies fractional differential problems by transforming them into algebraic formulas within the transform space. On the other hand, the HPM has the ability to discretize the nonlinear terms in fractional problems. The fractional orders are considered in the Caputo sense. The main purpose of this strategy is to use an alternative approach that has never been employed in the time-fractional Emden–Fowler model. This strategy does not require any variable or hypothesis constraints that ruin the physical nature of the actual problem. The derived series yields a convergent series using the Taylor series formula. The analytical data and visual illustrations for several kinds of fractional orders validate the effectiveness of the suggested scheme. The significant results demonstrate that our recommended strategy is quick and simple to use on fractional problems.