Homotopy Perturbation ρ-Laplace Transform Approach for Numerical Simulation of Fractional Navier-Stokes Equations (Contemporary Mathematics, 2025)
In this study, we tackle the time fractional discrete Navier-Stokes equation by employing the homotopy perturbation ρ-Laplace transform method (HPLTM), utilizing the Caputo-Katugampola fractional derivative of time. Additionally, we present graphical representations of the solution generated using Matlab software, comparing it with the exact solution for α = 1. We perform two test problems to verify and demonstrate the effectiveness of our approach. Our numerical findings and graphical analyses indicate that the proposed approach exhibits remarkable efficiency and simplicity, rendering it suitable for addressing a diverse array of challenges encountered in engineering and the sciences.
Keywords: Caputo-Katugampola fractional derivative; HPLTM; Mittag-Leffler function; fractional Navier-Stokes equation