An analytical solution to the time fractional Navier–Stokes equation based on the Katugampola derivative in Caputo sense by the generalized Shehu residual power series approach

Abstract

The Navier–Stokes equations describe the behavior of viscous fluids and establish a fundamental connection between the application of external forces on fluid motion and the resulting pressure within the fluid. The objective of this study is to solve the two-dimensional time fractional Navier–Stokes equation through the utilization of the residual power series method together with the generalized Shehu transform. The method is called the generalized Shehu residual power series (GSHRPS) approach. The fractional derivative utilized in this research is the Katugampola derivative in the sense of Caputo. The effectiveness of this method is verified by demonstrating its convergence to the solution of the previously described problem. Furthermore, a practical example is presented to show the precision, accuracy, and efficiency of this approach in order to illustrate its effectiveness and benefits.