Mild Solution for the Time-Fractional Navier–Stokes Equation Incorporating MHD Effects

Abstract

The Navier–Stokes (NS) equations involving MHD effects with time-fractional derivatives are discussed in this paper. This paper investigates the local and global existence and uniqueness of the mild solution to the NS equations for the time fractional differential operator. In addition, we work on the regularity effects of such types of equations which are caused by MHD flow.

Keywords

• Navier–Stokes equations
• mild solution
• existence and uniqueness
• Caputo fractional derivative
• Mittag–Leffler functions
• regularity