Controllability of neutral stochastic functional integro-differential equations driven by fractional brownian motion with Hurst parameter lesser than $ 1/2 $

Brahim Boufoussi; Soufiane Mouchtabih

doi:10.3934/eect.2020096

Article Contents

2021, Volume 10, Issue 4: 921-935. Doi: 10.3934/eect.2020096

This issue Previous Article Stabilization of higher order Schrödinger equations on a finite interval: Part I Next Article Optimal distributed control of the three dimensional primitive equations of large-scale ocean and atmosphere dynamics

Controllability of neutral stochastic functional integro-differential equations driven by fractional brownian motion with Hurst parameter lesser than $ 1/2 $

Brahim Boufoussi^1, and
Soufiane Mouchtabih^1, ,

1.
Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, 2390 Marrakesh, Morocco

^* Corresponding author: Soufiane Mouchtabih
^* Corresponding author: Soufiane Mouchtabih

Received: April 30, 2019

Revised: August 31, 2020

Early access: October 2020

Published: December 2021

Abstract Full Text(HTML) Related Papers Cited by

Abstract

This article investigates the controllability for neutral stochastic delay functional integro-differential equations driven by a fractional Brownian motion, with Hurst parameter lesser than $ 1/2 $. We employ the theory of resolvent operators developed by [10] combined with the Banach fixed point theorem to establish sufficient conditions to prove the desired result.

Keywords:

Mathematics Subject Classification: Primary: 60H15, 60G15, 93E03, 93B05.

Citation:

Full Text(HTML)

Related Papers

Cited by

References

[1]	H. M. Ahmed and J. Wang, Exact null controllability of Sobolev-type Hilfer fractional stochastic differential equations with fractional Brownian motion and Poisson jumps, Bull. Iran. Math. Soc., 44 (2018), 673-690. doi: 10.1007/s41980-018-0043-8.
[2]	M. A. Alqudah, C. Ravichandran, T. Abdeljawad and N. Valliammal, New results on Caputo fractional-order neutral differential inclusions without compactness, Adv Differ Equ, 2019 (2019), Paper No. 528, 14 pp. doi: 10.1186/s13662-019-2455-z.
[3]	P. Balasubramaniam, N. Kumaresan, K. Ratnavelu and P. Tamilalagan, Local and global existence of mild solution for impulsive fractional stochastic differential equations, Bull. Malays. Math. Sci. Soc., 38 (2015), 867-884. doi: 10.1007/s40840-014-0054-4.
[4]	A. Boudaoui and E. Lakhel, Controllability of stochastic impulsive neutral functional differential equations driven by fractional Brownian motion with infinite delay, Differ Equ Dyn Syst, 26 (2018), 247-263. doi: 10.1007/s12591-017-0401-7.
[5]	B. Boufoussi and S. Hajji, Transportation inequalities for neutral stochastic differential equations driven by fractional Brownian motion with Hurst parameter lesser than 1/2, Mediterr. J. Math., 14 (2017), Paper No. 192, 16 pp. doi: 10.1007/s00009-017-0992-9.
[6]	T. Caraballo and M. A. Diop, Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion, Front. Math. China, 8 (2013), 745-760. doi: 10.1007/s11464-013-0300-3.
[7]	A. Chadha and D. N. Pandey, Existence results for an impulsive neutral stochastic fractional integro-differential equation with infinite delay, Nonlinear Anal., 128 (2015), 149-175. doi: 10.1016/j.na.2015.07.018.
[8]	J. Cui and L. Yan, Controllability of neutral stochastic evolution equations driven by fractional Brownian motion, Acta Mathematica Scientia B, 37 (2017), 108-118. doi: 10.1016/S0252-9602(16)30119-9.
[9]	W. Desch, R. Grimmer and W. Schappacher, Some consideration for linear integro-differential equations, J. Math. Anal. Appl., 104 (1984), 219-234. doi: 10.1016/0022-247X(84)90044-1.
[10]	R. C. Grimmer, Resolvent operators for integral equations in a Banach space, Transactions of the American Mathematical Society, 273 (1982), 333-349. doi: 10.1090/S0002-9947-1982-0664046-4.
[11]	K. Jothimani, K. Kaliraj, Z. Hammouch and C. Ravichandran, New results on controllability in the framework of fractional integro-differential equations with nondense domain, Eur. Phys. J. Plus, 134 (2019).
[12]	E. H. Lakhel, Controllability of neutral stochastic functional integro-differential equations driven by fractional Brownian motion, Stoch. Ana. and App., 34 (2016), 427-440. doi: 10.1080/07362994.2016.1149718.
[13]	E. Lakhel, Controllability of impulsive neutral stochastic integro-differential systems driven by FBM with unbounded delay, Le Matematiche, 73 (2018), 319-339. doi: 10.4418/2018.73.2.6.
[14]	E. Lakhel and M. A. McKibben, Controllability for time-dependent neutral stochastic functional differential equations with Rosenblatt process and impulses, Int. J. Control Autom. Syst., 17 (2019), 286-297. doi: 10.1007/s12555-016-0363-5.
[15]	J. A. Machado, C. Ravichandran, M. Rivero and J. J. Trujillo, Controllability results for impulsive mixed-type functional integro-differential evolution equations with nonlocal conditions, Fixed Point Theory Appl, 2013 (2013), 16pp. doi: 10.1186/1687-1812-2013-66.
[16]	D. Nualart, The Malliavin Calculus and Related Topics, 2$^{nd}$ edition, Springer-Verlag, Berlin, 2006.
[17]	J. Pruss, Evolutionary Integral Equations and Applications, Birkhauser, Basel, 1993. doi: 10.1007/978-3-0348-8570-6.
[18]	C. Ravichandran, N. Valliammal and J. J. Nieto, New results on exact controllability of a class of fractional neutral integro-differential systems with state-dependent delay in Banach spaces, J.Franklin I., 356 (2019), 1535-1565. doi: 10.1016/j.jfranklin.2018.12.001.
[19]	Y. Ren, H. Dai and R. Sakthivel, Approximate controllability of stochastic differential system driven by a Levy process, Inter nat. J. Control, 86 (2013), 1158-1164. doi: 10.1080/00207179.2013.786188.
[20]	T. Sathiyaraj and P. Balasubramaniam, Controllability of fractional neutral stochastic integro-differential inclusions of order $p\in(0, 1]$, $q\in(1, 2]$ with fractional Brownian motion, Eur. Phys. J. Plus 131, 357 (2016).
[21]	P. Tamilalagan and P. Balasubramanniam, Approximate controllability of fractional stochastic differential equations driven by mixed fractional Brownian motion via resolvent operators, Int. J. of Control., 90 (2017), 1713-1727. doi: 10.1080/00207179.2016.1219070.
[22]	N. Valliammal, C. Ravichandran and J. H. Park, On the controllability of fractional neutral integro-differential delay equations with nonlocal conditions, Math. Methods Appl. Sci., 40 (2017), 5044-5055. doi: 10.1002/mma.4369.
[23]	J. Wang, Approximate mild solutions of fractional stochastic evolution equations in Hilbert spaces, Appl. Math. Comput., 256 (2015), 315-323. doi: 10.1016/j.amc.2014.12.155.