Advanced Search
Article Contents
Article Contents

Controllability of retarded time-dependent neutral stochastic integro-differential systems driven by fractional Brownian motion

  • *Corresponding author: Youssef Benkabdi

    *Corresponding author: Youssef Benkabdi 
Abstract Full Text(HTML) Related Papers Cited by
  • In this manuscript the controllability for a class of time-dependent neutral stochastic integro-differential systems driven by fractional Brownian motion in a separable Hilbert space with delay is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

    Mathematics Subject Classification: Primary: 35R10, 93B05, 60G22, 60H20.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] P. Acquistapace and B. Terreni, A unified approach to abstract linear parabolic equations, Tend. Sem. Mat. Univ. Padova, 78 (1987), 47-107. 
    [2] H. M. Ahmed, Semilinear neutral fractional neutral integro-diferential equations with monlocal conditions, J. Theor. Proba., 28 (2015), 667-680.  doi: 10.1007/s10959-013-0520-1.
    [3] D. Aoued and S. Baghli-Bendimerad, Mild solutions for Perturbed evolution equations with infinite state-dependent delay, Electron. J. Qual. Theory Differ. Equ., 2013 (2013), No. 59, 24 pp. doi: 10.14232/ejqtde.2013.1.59.
    [4] Y. Benkabdi and E. H. Lakhel, Controllability of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion with delay and Poisson jumps, Proyecciones (Antofagasta, On line), 40 (2021), 1521–1545. doi: 10.22199/issn.0717-6279-4596.
    [5] Y. Benkabdi and E. Lakhel, Controllability of impulsive neutral stochastic integro-differential systems driven by a Rosenblatt process with unbounded delay, Random Operators and Stochastic Equations, 29 (2021), 237-250.  doi: 10.1515/rose-2021-2063.
    [6] B. Boufoussi and S. Hajji, Neutral stochastic functional differential equation driven by a fractional Brownian motion in a Hilbert space, Statist. Probab. Lett., 82 (2012), 1549-1558.  doi: 10.1016/j.spl.2012.04.013.
    [7] J. Klamka, Controllability of Dynamical Systems, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1991.
    [8] J. Klamka, Relative and absolute controllability of discrete systems with delays in control, Int. J. Control., 26 (1977), 65-74.  doi: 10.1080/00207177708922289.
    [9] J. Klamka, Stochastic controllability of linear systems with delay in control, Bull. Pol. Acad. Sci. Tech. Sci., 55 (2007), 23-29. 
    [10] J. Klamka, Controllability of dynamical systems. A survey, Bull. Pol. Acad. Sci. Tech. Sci., 61 (2013), 221-229. 
    [11] J. Klamka, Constrained controllability of nonlinear systems, Journal of Mathematical Analysis and Applications, 201 (1996), 365-374.  doi: 10.1006/jmaa.1996.0260.
    [12] J. Klamka, Constrained exact controllability of semilinear systems, Systems and Control Letters, 47 (2002), 139-147. 
    [13] J. Klamka, Approximate constrained controllability of mechanical systems, Journal of Theoretical and Applied Mechanics, 43 (2005), 539-554. 
    [14] J. Klamka, Constrained controllability of semilinear systems with delays, Nonlinear Dynamics, 56 (2009), 169-177.  doi: 10.1007/s11071-008-9389-4.
    [15] E. Lakhel and M. A. McKibben, Controllability of neutral stochastic integro-differential evolution equations driven by a fractional Brownian motion, Afr. Mat., 28 (2017), 207-220.  doi: 10.1007/s13370-016-0439-7.
    [16] E. Lakhel and M. A. McKibben, Controllability for time-dependent neutral stochastic func- tional differential equations with Rosenblatt process and impulses, Int. J. Control Autom. Syst., 17 (2019), 286-297. 
    [17] Z. LiL. Xu and X. Li, On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays, Bull. Iranian Math. Soc., 42 (2016), 1479-1496. 
    [18] D. Nualart, The Malliavin Calculus and Related Topics, 2$^{nd}$ edition, Springer-Verlag, Berlin 2006.
    [19] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4612-5561-1.
    [20] K. RamkumarK. Ravikumar and K. Banupriya, Approximate controllability for time-dependent impulsive neutral stochastic partial integrodifferential equations with Poisson jumps, Discussiones Mathematicae: Differential Inclusions, Control and Optimization, 40 (2020), 61-74.  doi: 10.7151/dmdico.1222.
    [21] Y. RenX. Cheng and R. Sakthivel, On time-dependent stochastic evolution equations driven by fractional Brownian motion in Hilbert space with finite delay, Math. Methods Appl. Sci., 37 (2014), 2177-2184.  doi: 10.1002/mma.2967.
    [22] Y. RenQ. Zhou and L. Chen, Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay, J. Optim. Theory Appl., 149 (2011), 315-331.  doi: 10.1007/s10957-010-9792-0.
    [23] M. Röckner and T. Zhang, Stochastic evolution equation of jump type: Existence, uniqueness and large deviation principles, Potential Anal., 26 (2007), 255-279.  doi: 10.1007/s11118-006-9035-z.
    [24] R. SakthivelR. GaneshY. Ren and S. M. Anthoni, Approximate controllability of nonlinear fractional dynamical systems, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 3498-3508.  doi: 10.1016/j.cnsns.2013.05.015.
    [25] R. SakthivelY. RenA. Debbouche and N. I. Mahmudov, Approximate controllability of fractional stochastic differential inclusions with nonlocal conditions, Appl. Anal., 95 (2016), 2361-2382.  doi: 10.1080/00036811.2015.1090562.
    [26] T. Taniguchi and J. Luo, The existence and asymptotic behaviour of mild solutions to stochastic evolution equations with infinite delays driven by Poisson jumps, Stoch. Dyn., 9 (2009), 217-229.  doi: 10.1142/S0219493709002646.
  • 加载中

Article Metrics

HTML views(228) PDF downloads(251) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint