This paper addresses some results about mild solution to time-fractional Navier–Stokes equations with bounded delay existed in the convective term and external force. Based on Schauder’s fixed point theorem, we establish sufficient conditions for existence uniqueness of global Banach spaces. Moreover, polynomial decay estimate is given. Furthermore, approximate controllability obtained by const...

This study examines if there are any mild solutions for the perturbed partial functional and neutral evolution equations with state-dependent delay when derivative utilizes Caputo's fractional derivative, as well whether such unique. The solution itself determines how long take to solve. work proves existence uniqueness of these using semigroup theory Banach contraction theorem in spaces.

The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results. Nowadays, fractional calculus receives increasing at...