Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EXISTENCE AND EXPONENTIAL STABILITY OF NEUTRAL STOCHASTIC PARTIAL INTEGRODIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH IMPULSIVE EFFECTS

  • CHALISHAJAR, DIMPLEKUMAR (Department of Applied Mathematics, Mallory Hall, Virginia Military Institute) ;
  • RAMKUMAR, K. (Department of Mathematics, PSG College of Arts and Science) ;
  • ANGURAJ, A. (Department of Mathematics, PSG College of Arts and Science)
  • Received : 2021.10.09
  • Accepted : 2022.02.11
  • Published : 2022.03.30
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Abstract

The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

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References

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