沃尔泰拉型分数阶时滞动态系统的可控性准则
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摘要
本文考虑沃尔泰拉型非线性分数阶时滞动态系统的可控性结果。给出一类沃尔泰拉型分数阶时滞动态系统的解的定义,利用Schauder不动点定理,建立该分数阶时滞动态系统的可控性准则。最后,用示例来说明结果的有效性。
In this paper,we consider controllability results of nonlinear fractional delay dynamical systems of Volterra Type.The definition of solution of a class of fractional delay dynamical systems of Volterra type is given,and controllability criteria of the fractional delay dynamical systems are obtained by Schauder fixed point theorem.At last,An examples is presented to illustrate effectiveness of the main results.
In this paper,we consider controllability results of nonlinear fractional delay dynamical systems of Volterra Type.The definition of solution of a class of fractional delay dynamical systems of Volterra type is given,and controllability criteria of the fractional delay dynamical systems are obtained by Schauder fixed point theorem.At last,An examples is presented to illustrate effectiveness of the main results.
引文
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[11] JIANG J Q,LIU L S,WU Y H.Symmetric positive solutions to singular system with multi-point coupled boundary conditions[J].Applied and Computational Mathematics,2013,220(4):536-548.
[12] GUO L M,LIU L S,WU Y H.Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions[J].Nonlinear Analysis-Modeling and Control,2016,21(5):635-650.
[13] ZHU B,LIU L S,WU Y H.Local and global existence of mild solutions for a class of nonlinear fractional reaction-diffusion equation with delay[J].Applied Mathematics Letters,2016,61:73-79.
[14] NIRMALA R J,BALACHANDRAN K,GERMA L R,et al. Controllability of nonlinear fractional delay dynamical systems[J].Reports on Mathematical Physics,2016,77(1):87-104.
[15] NIRMALA R J,BALACHANDRAN K.Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control[J].Kybernetika,2017,53(1):161-178.
[16] GOU H D,LI B L.Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay[J].Journal of Inequalities and Applications,2017,252:1-20.
[17] QIN H Y,ZUO X,LIU J W.Some new generalized retarded Gronwall-like inequalities and their applications in nonlinear systems[J].Journal of Control Science and Engineering,2016,2016:1-8.
[2] QIN H Y,ZUO X,LIU J W,et al.Approximate controllability and optimal controls of fractional dynamical systems of order 1
[4] QIN H Y,ZHANG C H,LI T X,et al.Controllability of abstract fractional differential evolution equations with nonlocal conditions[J].Journal of Mathematics and Computer Science-JMCS,2017,17:293-300.
[5] JIANG C M,ZHANG F F,QIN H Y,et al.Anti-synchronization of fractional order chaotic complex systems with unknown parameters via adaptive control[J].Journal of Nonlinear Sciences and Applications,2017,10:5608-5621.
[6] LIU L S,LI H D,LIU C,et al.Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary value problems[J].Journal of Nonlinear Sciences and Applications,2017,10:243-262.
[7] ZHANG X G,LIU L S,WU Y H,et al.Nontrivial solutions for a fractional advection dispersion equation in anomalous diffusion[J].Applied Mathematics Letters,2017,66:1-8.
[8] ZHANG X G,MAO C L,LIU L S,et al.Exact iterative solution for an abstract fractional dynamic system model for bioprocess[J].Qualitative Theory of Dynamical Systems,2017,16:205-222.
[9] ZHANG X G,LIU L S,WU Y H.The entire large solutions for aquasilinear Schr?dinger elliptic equation by the dual approach[J].Applied Mathematics Letters,2016,55:1-9.
[10] JIANG J Q,LIU L S,WU Y H.Positive solutions for second-order differential equations with integral boundary conditions[J].Bulletin of the Malaysian Mathematical Sciences Society,2014,37(3):779-796.
[11] JIANG J Q,LIU L S,WU Y H.Symmetric positive solutions to singular system with multi-point coupled boundary conditions[J].Applied and Computational Mathematics,2013,220(4):536-548.
[12] GUO L M,LIU L S,WU Y H.Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions[J].Nonlinear Analysis-Modeling and Control,2016,21(5):635-650.
[13] ZHU B,LIU L S,WU Y H.Local and global existence of mild solutions for a class of nonlinear fractional reaction-diffusion equation with delay[J].Applied Mathematics Letters,2016,61:73-79.
[14] NIRMALA R J,BALACHANDRAN K,GERMA L R,et al. Controllability of nonlinear fractional delay dynamical systems[J].Reports on Mathematical Physics,2016,77(1):87-104.
[15] NIRMALA R J,BALACHANDRAN K.Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control[J].Kybernetika,2017,53(1):161-178.
[16] GOU H D,LI B L.Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delay[J].Journal of Inequalities and Applications,2017,252:1-20.
[17] QIN H Y,ZUO X,LIU J W.Some new generalized retarded Gronwall-like inequalities and their applications in nonlinear systems[J].Journal of Control Science and Engineering,2016,2016:1-8.