Abstract
The present work addresses some new controllability results for a class of fractional integrodifferential dynamical systems with a delay in Banach spaces. Under the new definition of controllability , first introduced by us, we obtain some sufficient conditions of controllability for the considered dynamic systems. To conquer the difficulties arising from time delay, we also introduce a suitable delay item in a special complete space. In this work, a nonlinear item is not assumed to have Lipschitz continuity or other growth hypotheses compared with most existing articles. Our main tools are resolvent operator theory and fixed point theory. At last, an example is presented to explain our abstract conclusions.
Highlights
The purpose of this work is to investigate the controllability of the following fractional integrodifferential dynamical systems with a delay in Banach spaces:
Some new controllability results for a class of fractional integrodifferential dynamical systems with a delay in Banach spaces are derived in this paper by using resolvent operator theory and fixed-point theory
A suitable delay item in a special complete space is introduced to solve the difficulties caused by time delay
Summary
The purpose of this work is to investigate the controllability of the following fractional integrodifferential dynamical systems with a delay in Banach spaces: C r. Z(t) = ψ(t), t ∈ [−c, 0], where the state variable z(·) takes values in Banach space E. C Dr denotes the Caputo derivative with order r ∈ (0, 1). A : D (A) ⊂ E → E is a closed linear unbounded operator on E. x is a control function defined in L2 (V; U ), where U is a Banach space. B : U → E is a bounded linear operator. G is a given nonlinear item satisfying some appropriate hypotheses and Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in Hz (t) =.
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