Home Existence of solutions for fractional impulsive neutral functional differential equations driven by fractional Brownian motion
Article
Licensed
Unlicensed Requires Authentication

Existence of solutions for fractional impulsive neutral functional differential equations driven by fractional Brownian motion

  • Ahmed Lahmoudi and El Hassan Lakhel EMAIL logo
Published/Copyright: May 31, 2022

Abstract

In this paper, we consider a class of fractional impulsive neutral stochastic functional differential equations with infinite delay driven by a fractional Brownian motion in a real separable Hilbert space. We prove the existence of mild solutions by using stochastic analysis and a fixed-point strategy.


Communicated by Stanislav Molchanov


Acknowledgements

The authors would like to thank the referee and the editor for their careful comments and valuable suggestions on this work.

References

[1] Y. Benkabdi and E. Lakhel, Controllability of impulsive neutral stochastic integro-differential systems driven by a Rosenblatt process with unbounded delay, Random Oper. Stoch. Equ. 29 (2021), no. 4, 237–250. 10.1515/rose-2021-2063Search in Google Scholar

[2] F. Biagini, Y. Hu, B. Øksendal and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, Springer, London, 2008. 10.1007/978-1-84628-797-8Search in Google Scholar

[3] B. Boufoussi and S. Hajji, Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space, Statist. Probab. Lett. 82 (2012), 1549–1558. 10.1016/j.spl.2012.04.013Search in Google Scholar

[4] B. Boufoussi, S. Hajji and E. Lakhel, Functional differential equations in Hilbert spaces driven by a fractional Brownian motion, Afr. Mat. 23 (2012), no. 2, 173–194. 10.1007/s13370-011-0028-8Search in Google Scholar

[5] E. Lakhel, Controllability of neutral stochastic functional integro-differential equations driven by fractional Brownian motion, Stoch. Anal. Appl. 34 (2016), no. 3, 427–440. 10.1080/07362994.2016.1149718Search in Google Scholar

[6] E. Lakhel and 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), no. 1, 14–29. Search in Google Scholar

[7] E. Lakhel and M. A. McKibben, Existence of solutions for fractional neutral functional differential equations driven by fBm with infinite delay, Stochastics 90 (2018), 313–329. 10.1080/17442508.2017.1346657Search in Google Scholar

[8] Y. Li and B. Liu, Existence of solution of nonlinear neutral functional differential inclusion with infinite delay, Stoch. Anal. Appl. 25 (2007), 397–415. 10.1080/07362990601139610Search in Google Scholar

[9] B. Mandelbrot and V. Ness, Fractional Brownian motion, fractional noises and applications, SIAM Rev. 10 (1986), no. 4, 422–437. 10.1137/1010093Search in Google Scholar

[10] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983. 10.1007/978-1-4612-5561-1Search in Google Scholar

[11] Y. Zhou and J. Feng, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl. 59 (2010), 1063–1077. 10.1016/j.camwa.2009.06.026Search in Google Scholar

Received: 2021-07-20
Accepted: 2022-04-02
Published Online: 2022-05-31
Published in Print: 2022-10-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 1.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/rose-2022-2080/html?lang=en
Scroll to top button