New approximate analytical technique for the solution of time fractional fluid flow models

Umar Farooq,Haifa Bin Jebreen,Evren Hincal,Hassan Khan,Hassan Khan,Fairouz Tchier,Dumitru Baleanu

doi:10.1186/s13662-021-03240-z

Abstract

In this note, we broaden the utilization of an efficient computational scheme called the approximate analytical method to obtain the solutions of fractional-order Navier–Stokes model. The approximate analytical solution is obtained within Liouville–Caputo operator. The analytical strategy generates the series form solution, with less computational work and fast convergence rate to the exact solutions. The obtained results have shown a simple and useful procedure to analyze complex problems in related areas of science and technology.

Highlights

The old idea of fractional-order derivatives became the focal point for many researchers
We develop the approximate analytical method (AAM) based on an analytical strategy using the Riemann–Liouville integral operator and Caputo operator (4)
5 Conclusion In this paper, we applied a newly developed approximate analytical method based on the iterative procedure and the properties of Caputo and Riemann–Liouville integral operators

Summary

Introduction

The old idea of fractional-order derivatives became the focal point for many researchers. Using the Riemann–Liouville fractional partial integral operator of order θ with respect to t on both sides of equation (12) and using the properties of the Riemann–Liouuille fractional order operator (4), we obtain υλ( , , ξ , t) = υ( , , ξ , 0) + λItθ Lυ( , , ξ , t) + אυ( , , ξ , t) + g( , , ξ , t) . Example 4.1 Consider the time fractional-order Naiver–Stokes model along with initial source in the form [22];

Results

Conclusion