Exact controllability of fractional order evolution equations in Banach spaces

Abstract

Abstract In this paper, we deal with the exact controllability of a class of fractional evolution equations with time-varying delay. Under the nonlocal condition, the exact controllability of this system is established by applying a Leray–Schauder alternative theorem and the theory of propagation families in a Banach space. As an application, the controllability of a fractional partial differential equation is examined to show the effectiveness of our result.

Keywords

• Fractional order evolution equation
• Caputo fractional derivative
• Banach space