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 uniqueness of mild solution to NS for time fractional differential operator. In addition, we work on regularity such types which caused by flow.

In this paper we study the growth of mild solutions of abstract Cauchy problems governed by a densely defined generator A of an o-times integrated semigroup {Sa(t)},>o. We prove the following results: (i) If lIsa( I Me wt for ime M > 0, w E W, and all t 2 0, then for all E > 0, o > 0 and zo E D((-Aw+o)a+E) a unique mild solution exists. Moreover, this solution is exponentially bounded, and its ...

A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of T0-periodic PC-mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative res...