Mild Solutions To The Time Fractional Navier-Stokes Delay Differential Inclusions

In this paper,we study a Navier-Stokes delay differential inclusion with time fraction-al derivative of order ??(0,1).We first prove the local and global existence,decay and regularity properties of mild solutions when the initial data belongs to C([-h,0];D(A??)).The fractional resolvent operator theory and some techniques of measure of noncompact-ness are successfully applied to obtain the results.An example is also given to illustrate the feasibility of our abstract results.