Abstract
We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce thePC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results.
Highlights
The concept of controllability plays an important part in the analysis and design of control systems
Since Kalman [1] first introduced its definition in 1963, controllability of the deterministic and stochastic dynamical control systems in finite-dimensional and infinite-dimensional spaces is well developed in different classes of approaches, and more details can be found in papers [2,3,4]
The purpose of this paper is to provide some suitable sufficient conditions for the existence of mild solutions and approximate controllability results for the impulsive fractional abstract Cauchy problems with Riemann-Liouville fractional derivatives
Summary
The concept of controllability plays an important part in the analysis and design of control systems. Some authors [5,6,7] have studied the exact controllability for nonlinear evolution systems by using the fixed point theorems. It is shown that the concept of exact controllability is difficult to be satisfied in infinite-dimensional space. It is important to study the weaker concept of controllability, namely, approximate controllability for differential equations. In these years, several researchers [9,10,11,12,13,14,15,16,17] have studied it for control systems
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