Time-fractional (2+1)-dimensional navier-stokes equations: similarity reduction and exact solutions for one-parameter lie group of rotations

Abstract

Abstract The current study is dedicated to solving the time-fractional (2+1)-dimensional Navier–Stokes model. The model has wide applications in blood flow, in the design of power stations, weather prediction, ocean currents, water flow in a pipe, air flow around the aircraft wings, the analysis of pollution, and many other areas of engineering. The Lie symmetry approach is applied to the governed time-fractional equation to fulfill this need. In the direction of exact solutions of the time-fractional equation first of all invariance condition is obtained in the presence of the Lie group. Consequently, infinitesimals are obtained with the help of the invariant condition. Moreover, these infinitesimals are utilized to obtain the subalgebras. Further, under each subalgebras similarity variables and similarity solutions are obtained which are used to find the reduced equations. These reduced equations are solved for exact solutions. The solutions of the reduced equations are further used to find the exact solutions of the main time-fractional (2+1)-dimensional Navier–Stokes equation with the help of similarity solutions under each subalgebra.