Work

Using the Natural Generalized Laplace Transform to Solve the Time-Fractional Navier–Stokes Equation

Year: 2026

Type: article

Abstract: This article proposes a novel approach for dealing with the time-fractional Navier–Stokes equations via the natural generalized Laplace transform decomposition method (NGLTDM). This hybrid method utilizes both the natural generalized Laplace transform (NGLT) and a decomposition method. The method is correct because the series solutions become more accurate when more terms are added. We establish precise theorems that verify the existence of solutions and the convergence of the series. The analysis shows that the suggested method is more general than the Homotopy Perturbation Method (HPM) and the Adomian Decomposition Method (ADM). Also, this approach can be applied to handle difficult fluid dynamics problems governed by the Navier–Stokes equations. This study enhances analytical methodologies for fractional-order flow models.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10050285

Author: Hassan Eltayeb

Institution: King Saud University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: King Saud University