Approximate controllability of impulsive fractional integro-differential equation with state-dependent delay in Hilbert spaces

被引:18
作者
Zhou, Yong [1 ,2 ]
Suganya, S. [3 ]
Arjunan, M. Mallika [3 ]
Ahmad, B. [2 ]
机构
[1] Xiangtan Univ, Dept Math, Xiangtan 411105, Hunan, Peoples R China
[2] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia
[3] CBM Coll, Dept Math, Coimbatore 641042, Tamil Nadu, India
基金
中国国家自然科学基金;
关键词
approximate controllability; fractional-order differential equations; impulsive conditions; state-dependent delay; semigroup theory; Banach contraction principle; FUNCTIONAL-DIFFERENTIAL EQUATIONS; EVOLUTION INCLUSIONS; EXISTENCE;
D O I
10.1093/imamci/dnx060
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, the problem of approximate controllability for non-linear impulsive fractional integro-differential equation with state-dependent delay in Hilbert spaces is investigated. We study the approximate controllability for non-linear impulsive integro-differential systems under the assumption that the corresponding linear control system is approximately controllable. By utilizing the methods of fractional calculus, semigroup theory, fixed-point theorem coupled with solution operator, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.
引用
收藏
页码:603 / 622
页数:20
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