Approximate Controllability of Fractional Differential Equations with State-Dependent Delay

被引:68
|
作者
Rathinasamy, Sakthivel [1 ]
Yong, Ren [2 ]
机构
[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea
[2] Anhui Normal Univ, Dept Math, Wuhu 241000, Peoples R China
基金
中国国家自然科学基金;
关键词
Nonlinear fractional systems; state-dependent delay; approximate controllability; INTEGRODIFFERENTIAL EQUATIONS; CONSTRAINED CONTROLLABILITY; EVOLUTION-EQUATIONS; SEMILINEAR SYSTEMS; INCLUSIONS; EXISTENCE;
D O I
10.1007/s00025-012-0245-y
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The systems governed by delay differential equations come up in different fields of science and engineering but often demand the use of non-constant or state-dependent delays. The corresponding model equation is a delay differential equation with state-dependent delay as opposed to the standard models with constant delay. The concept of controllability plays an important role in physics and mathematics. In this paper, first we study the approximate controllability for a class of nonlinear fractional differential equations with state-dependent delays. Then, the result is extended to study the approximate controllability fractional systems with state-dependent delays and resolvent operators. A set of sufficient conditions are established to obtain the required result by employing semigroup theory, fixed point technique and fractional calculus. In particular, the approximate controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is approximately controllable. Also, an example is presented to illustrate the applicability of the obtained theory.
引用
收藏
页码:949 / 963
页数:15
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