Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion
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Authors
El Hassan Lakhel
- National School of Applied Sciences, Cadi Ayyad University, 46000 Safi, Morocco.
Abdelmonaim Tlidi
- National School of Applied Sciences, Cadi Ayyad University, 46000 Safi, Morocco.
Abstract
In this paper, we consider the controllability of certain class of
non-autonomous neutral evolution stochastic functional
differential equations, with time varying delays, driven by a
fractional Brownian motion in a separable real Hilbert space.
Sufficient conditions for controllability are obtained by employing
a fixed point approach. A practical example is provided to
illustrate the viability of the abstract result of this work.
Share and Cite
ISRP Style
El Hassan Lakhel, Abdelmonaim Tlidi, Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 6, 850--863
AMA Style
Lakhel El Hassan, Tlidi Abdelmonaim, Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion. J. Nonlinear Sci. Appl. (2018); 11(6):850--863
Chicago/Turabian Style
Lakhel, El Hassan, Tlidi, Abdelmonaim. "Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion." Journal of Nonlinear Sciences and Applications, 11, no. 6 (2018): 850--863
Keywords
- Controllability
- neutral stochastic functional differential equations
- evolution operator
- fractional Brownian motion
MSC
References
-
[1]
P. Acquistapace, B. Terreni, A unified approach to abstract linear parabolic equations, Rend. Sem. Mat. Univ. Padova, 78 (1987), 47–107.
-
[2]
D. Aoued, S. Baghli-Bendimerad, Mild solutions for Perturbed evolution equations with infinite state-dependent delay, Electron. J. Qual. Theory Differ. Equ., 2013 (2013), 24 pages.
-
[3]
G. Arthi, K. Balachandran , Controllability of second-order impulsive functional differential equations with state-dependent delay, Bull. Korean Math. Soc., 48 (2011), 1271–1290.
-
[4]
K. Balachandran, J. Y. Park, S. H. Park , Controllability of nonlocal impulsive quasilinear integrodifferential systems in Banach spaces , Rep. Math. Phys., 65 (2010), 247–257
-
[5]
P. Balasubramaniam, J. P. Dauer , Controllability of semilinear stochastic delay evolution equations in Hilbert spaces, Int. J. Math. Math. Sci., 31 (2002), 157–166.
-
[6]
B. Boufoussi, S. Hajji, Neutral stochastic functional differential equation driven by a fractional Brownian motion in a Hilbert space, Statist. Probab. Lett., 82 (2012), 1549–1558.
-
[7]
B. Boufoussi, S. Hajji, E. H. Lakhel , Functional differential equations in Hilbert spaces driven by a fractional Brownian motion, Afr. Mat., 23 (2012), 173–194.
-
[8]
B. Boufoussi, S. Hajji, E. Lakhel, Time-dependent Neutral stochastic functional differential equation driven by a fractional Brownian motion in a Hilbert space, Commun. Stochastic Anal., 10 (2016), 1–12.
-
[9]
Y.-K. Chang, A. Anguraj, M. Mallika Arjunan, Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces, Chaos Solitons & Fractals, 39 (2009), 1864–1876.
-
[10]
J. Klamka , Stochastic controllability of linear systems with delay in control, Bull. Pol. Acad. Sci. Tech. Sci., 55 (2007), 23–29.
-
[11]
A. N. Kolmogoroff, Wienersche spiralen und einige andere interessante kurven im Hilbertschen raum , (German) C. R. (Doklady) Acad. Sci. URSS (N.S.), 26 (1940), 115–118.
-
[12]
E. H. Lakhel , Controllability of Neutral Stochastic Functional Integro-Differential Equations Driven By Fractional Brownian Motion, Stoch. Anal. Appl., 34 (2016), 427–440.
-
[13]
E. H. Lakhel, Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps, Random Oper. Stoch. Equ., 24 (2016), 113–127.
-
[14]
E. Lakhel, S. Hajji , Existence and Uniqueness of Mild Solutions to Neutral SFDEs driven by a Fractional Brownian Motion with Non-Lipschitz Coefficients , J. Numer. Math. Stoch., 7 (2015), 14–29.
-
[15]
E. Lakhel, M. A. McKibben , Controllability of Impulsive Neutral Stochastic Functional Integro-Differential Equations Driven by Fractional Brownian Motion, Chapter 8 In book: Brownian Motion: Elements, Dynamics, and Applications, Editors: M. A. McKibben & M. Webster. Nova Science Publishers,New York , (2015), 131–148.
-
[16]
B. B. Mandelbrot, J. W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10 (1968), 422–437.
-
[17]
N. I. Mahmudov , Controllability of semilinear stochastic systems in Hilbert spaces , J. Math. Anal. Appl., 288 (2003), 197–211.
-
[18]
D. Nualart, The Malliavin Calculus and Related Topics, second edition, Springer-Verlag, Berlin (2006)
-
[19]
M. D. Quinn, N. Carmichael , An approach to non linear control problems using fixed point methods, degree theory and pseudo-inverses, Numer. Funct. Anal. Optim., 7 (1985), 197–219.
-
[20]
Y. Ren, X. Cheng, 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.
-
[21]
Y. Ren, L. Hu, R. Sakthivel, Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay, J. Comput. Appl. Math., 235 (2011), 2603–2614.
-
[22]
Y. Ren, D. Sun , Second-order neutral impulsive stochastic differential equations with delay, J. Math. Phys., 50 (2009), 102709.
-
[23]
Y. Ren, Q. Zhou, L. Chen , Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay, J. Optim. Theory, 149 (2011), 315–331.
-
[24]
R. Sakthivel , Complete controllability of stochastic evolution equations with jumps, Rep. Math. Phys., 68 (2011), 163–174.
-
[25]
R. Sathya, K. Balachandran, Controllability of nonlocal impulsive stochastic quasilinear integrodifferential systems, Electron. J. Qual. Theory Differ. Equ., 2011 (2011), 16 pages.