An approximate analytical solution of the time-fractional Navier–Stokes equations by the generalized Laplace residual power series method

Abstract

The dynamics of viscous fluids may be elucidated via the Navier–Stokes equations, which create a fundamental relationship between the exertion of external forces upon fluid motion and the resultant fluid pressure. This article examines the time-fractional Navier–Stokes equations by substituting the time derivative with the Katugampola fractional derivative represented in the Caputo type. The analytical solution for the time-fractional Navier–Stokes equation is obtained using the generalized Laplace residual power series technique. The proof of convergence to the solution of the proposed approach is established. To demonstrate the efficacy and precision of this methodology, two instances of time-fractional Navier–Stokes equations, which depict the movement of fluid inside a conduit, are shown. A comparative analysis is conducted between our findings and prior research outcomes.