## THERMAL SCIENCE

International Scientific Journal

### GENERATION AND SOLUTIONS TO THE TIME-SPACE FRACTIONAL COUPLED NAVIER-STOKES EQUATIONS

**ABSTRACT**

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.

**KEYWORDS**

PAPER SUBMITTED: 2020-03-24

PAPER REVISED: 2020-05-18

PAPER ACCEPTED: 2020-05-28

PUBLISHED ONLINE: 2020-11-27

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Issue 6**, PAGES [3899 - 3905]

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