Impulsive neutral functional differential equations driven by a fractional Brownian motion with unbounded delay

Abstract

In this paper, we prove the local and global existence and attractivity of mild solutions for stochastic impulsive neutral functional differential equations with infinite delay, driven by fractional Brownian motion.

Keywords:

• Fractional Brownian motion
• fixed point
• mild solutions
• attractivity
• neutral stochastic functional differential equation

AMS Subject Classifications:

• 35A01
• 34A37
• 60H15
• 60H20

Acknowledgements

We would like to thank the referees for the helpful suggestions and comments which allowed us to improve the presentation of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by FEDER and Ministerio de Economía y Competitividad [grant number MTM2011-22411]; Junta de Andalucía under Proyecto de Excelencia [P12-FQM-1492], [Number FQM314] (Spain).