TY - JOUR
TI - Generation and solutions to the time-space fractional coupled Navier-Stokes equations
AU - Lu Chang-Na
AU - Chang Sheng-Xiang
AU - Xie Luo-Yan
AU - Zhang Zong-Guo
JN - Thermal Science
PY - 2020
VL - 24
IS - 6
SP - 3899
EP - 3905
PT - Article
AB - In this paper, a Lagrangian of the coupled Navier-Stokes equations is  proposed based on the semi-inverse method. The fractional derivatives in the  sense of Riemann-Liouville definition are used to replace the classical  derivatives in the Lagrangian. Then the fractional Euler-Lagrange equation  can be derived with the help of the fractional variational principles. The  Agrawal's method is devot­ed to lead to the time-space fractional coupled  Navier-Stokes equations from the above Euler-Lagrange equation. The solution  of the time-space fractional coupled Navier-Stokes equations is obtained by  means of RPS algorithm. The numerical results are presented by using exact  solutions.