Afrika Matematika

, Volume 29, Issue 1–2, pp 233–247 | Cite as

Exponential stability of impulsive neutral stochastic functional differential equation driven by fractional Brownian motion and Poisson point processes

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Abstract

In this paper we consider a class of impulsive neutral stochastic functional differential equations with variable delays driven simultaneously by a fractional Brownian motion and a Poisson point processes in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point theory. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

Keywords

Mild solution Impulsive neutral stochastic differential equations Fractional powers of closed operators Fractional Brownian motion Poisson point processes 

Mathematics Subject Classification

60H15 60G22 60J75 

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  • Brahim Boufoussi
    • 1
  • Salah Hajji
    • 2
  • El Hassan Lakhel
    • 3
  1. 1.Department of Mathematics, Faculty of Sciences SemlaliaCadi Ayyad UniversityMarrakeshMorocco
  2. 2.Department of MathematicsRegional Center for the Professions of Education and TrainingMarrakeshMorocco
  3. 3.National School of Applied SciencesCadi Ayyad UniversitySafiMorocco

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