Abstract
In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the (alpha ,beta )-resolvent operator, we concern with the term u'(cdot ) and finding a control v such that the mild solution satisfies u(b)=u_{b} and u'(b)=u'_{b}. Finally, we present an application to support the validity study.
Highlights
1 Introduction Fractional differential equations have been applied to various fields successfully, for example, physics, engineering, and finance
Controllability plays a significant role in the evolution of modern mathematical control theory
This is a qualitative property of dynamical control systems and is of appropriate significance in control theory
Summary
Fractional differential equations have been applied to various fields successfully, for example, physics, engineering, and finance. Heping Ma and Biu Liu [20] interpreted the exact controllability and continuous dependence of fractional neutral integro-differential equations with state-dependent delay in Banach spaces. Yan [27] discussed the approximate controllability of neutral integro-differential delay systems with inclusion type in Hilbert space by using the fixed point theorem of discontinuous multi-valued operators supported by the Dhage fixed point technique with the resolvent operator. There is no work that reported on the problem of controllability of nonlinear fractional dynamical system of order 1 < α < 2, to the best of our knowledge, up until now the controllability for a class of impulsive fractional integro-differential evolution equation with fractional derivative of order α ∈
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