Approximate controllability for fractional semilinear parabolic equations

Abstract

In this paper, we deal with the control systems described by a large class of fractional semilinear parabolic equations. Firstly, we reformulate the fractional parabolic equations into abstract fractional differential equations associated with a semigroup on an appropriate Banach space. Secondly, we introduce a suitable concept on a mild solution for this kind of fractional parabolic equations and present the existence and uniqueness of mild solution by utilizing the theory of semigroup of linear operator, nonlinear analysis method and fixed point theorem. Then, the approximate controllability of the fractional semilinear parabolic equations is formulated and proved. At the end of the paper, an example is given to illustrate our main results.