1Prince Abdullah Bin Ghazi Faculty of Science & IT Al-Balqa' Applied University Salt – Jordan E-mail: odibat@bau.edu.jo
2Department of Mathematics Mutah University, P. O. Box 7 Al-Karak – Jordan E-mail: shahermm@yahoo.com
The time-fractional Navier-Stockes equations are obtained from the standard Navier-Stokes equations by replacing the first order derivative in time by a fractional derivative of order 0 < α < 1. The fractional derivative is considered in the Caputo sense. In this paper we derive analytical solutions for the time-fractional Navier-Stockes equations in a circular tube with help of Laplace and finite Hankel transforms. Detailed expressions for the solutions are well constructed in the form of a convergent series. In addition, exact solutions for three special cases have been obtained.
time-fractional Navier-Stokes equations, Caputo fractional derivative, Mittag-Leffler function
