A hybrid analytical technique for solving multi-dimensional time-fractional Navier-Stokes system

Abstract

In this research, a hybrid method, entitled the Laplace Residual Power Series technique, is adapted to find series solutions to a time-fractional model of Navier-Stokes equations in the sense of Caputo derivative. We employ the proposed method to construct analytical solutions to the target problem using the idea of the Laplace transform and the residual function with the concept of limit at infinity. A simple modification of the suggested method is presented to deal easily with the nonlinear terms constructed on the properties of the power series. Three interesting examples are solved and compared with the exact solutions to test the reliability, simplicity, and capacity of the presented method of solving systems of fractional partial differential equations. The results indicate that the used technique is a simple approach for solving nonlinear fractional differential equations since it depends only on the residual functions and the concept of the limit at infinity without needing differentiation or other complex computations.