EXISTENCE AND APPROXIMATE CONTROLLABILITY OF FRACTIONAL EVOLUTION EQUATIONS WITH NONLOCAL CONDITIONS VIA RESOLVENT OPERATORS

被引：77
作者：
Chen, Pengyu [1 ]
Zhang, Xuping [1 ]
Li, Yongxiang [1 ]
机构：
[1] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2020年 / 23卷 / 01期
关键词：
approximate controllability; fractional evolution equations; nonlocal conditions; alpha-order solution operator; alpha-order resolvent operator; CAUCHY-PROBLEMS; DIFFERENTIAL-EQUATIONS; MILD SOLUTIONS; SYSTEMS; INCLUSIONS;
D O I：
10.1515/fca-2020-0011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introducing a new Green's function and constructing a control function involving Gramian controllability operator. The discussions are based on Schauder's fixed point theorem as well as the theory of alpha-order solution operator and alpha-order resolvent operator. An example is given to illustrate the feasibility of our theoretical results.
引用
收藏
页码：268 / 291
页数：24
相关论文
共 51 条
[31]   Controllability of fractional integro-differential evolution equations with nonlocal conditions [J].
Liang, Jin ;
Yang, He .
APPLIED MATHEMATICS AND COMPUTATION, 2015, 254 :20-29
[32]   APPROXIMATE CONTROLLABILITY FOR NONLINEAR EVOLUTION HEMIVARIATIONAL INEQUALITIES IN HILBERT SPACES [J].
Liu, Zhenhai ;
Li, Xiuwen ;
Motreanu, Dumitru .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2015, 53 (05) :3228-3244
[33]   APPROXIMATE CONTROLLABILITY OF FRACTIONAL EVOLUTION SYSTEMS WITH RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES [J].
Liu, Zhenhai ;
Li, Xiuwen .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2015, 53 (04) :1920-1933
[34]  
Podlubny I., 1999, FRACTIONAL DIFFERENT
[35]   Identification of fractional systems using an output-error technique [J].
Poinot, T ;
Trigeassou, JC .
NONLINEAR DYNAMICS, 2004, 38 (1-4) :133-154
[36]  
Pruss J. W., 1993, Evolutionary integral equations and applications, DOI 10.1007/978-3-0348-8570-6
[37]   Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems [J].
Rossikhin, YA ;
Shitikova, MV .
ACTA MECHANICA, 1997, 120 (1-4) :109-125
[38]   A study on the mild solution of impulsive fractional evolution equations [J].
Shu, Xiao-Bao ;
Shi, Yajing .
APPLIED MATHEMATICS AND COMPUTATION, 2016, 273 :465-476
[39]   Some Applications of Fractional Calculus in Suppression of Chaotic Oscillations [J].
Tavazoei, Mohammad Saleh ;
Haeri, Mohammad ;
Jafari, Saeid ;
Bolouki, Sadegh ;
Siami, Milad .
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 2008, 55 (11) :4094-4101
[40]  
Valerio D., 2019, HDB FRACTIONAL CAL A, V6, P149
123456