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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.

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Authors and Affiliations

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

    Brahim Boufoussi

  2. Department of Mathematics, Regional Center for the Professions of Education and Training, Marrakesh, Morocco

    Salah Hajji

  3. National School of Applied Sciences, Cadi Ayyad University, 46000, Safi, Morocco

    El Hassan Lakhel

Authors
  1. Brahim Boufoussi
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  2. Salah Hajji
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  3. El Hassan Lakhel
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Correspondence to Salah Hajji.

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Boufoussi, B., Hajji, S. & Lakhel, E.H. Exponential stability of impulsive neutral stochastic functional differential equation driven by fractional Brownian motion and Poisson point processes. Afr. Mat. 29, 233–247 (2018). https://doi.org/10.1007/s13370-017-0538-0

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  • DOI: https://doi.org/10.1007/s13370-017-0538-0

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