Fractional analysis of time-fractional Emden–Fowler model arising in fluid flow of porous media and physical sciences

The concept of time-fractional Emden–Fowler (EF) model is used to describe the fluid flow in porous media, where the flow displays fractional-order behavior due to intricate microstructures. This study aims to analyze the fractional analysis of a linear and nonlinear time-fractional EF model, in which the fractional derivatives are taken in the Caputo form. We establish the Sumudu perturbation transform method (SPTM) by combining the Sumudu transform (ST) with the homotopy perturbation method (HPM). The ST discretizes the fractional-order model to a Sumudu space where the utilization of HPM handles the nonlinear parameters in the recurrence relation very effectively. We provide two numerical tests of the time-fractional EF model to check the legitimacy and reliability of the suggested scheme. The derived outcomes by SPTM enhance the excellence over a longer period by reducing the parameters of the truncated series. Some graphical representations at different fractional orders are provided to validate our proposed scheme. This approach offers a clear and concise procedure with symbolic computation to derive the series results which converge very promptly.