Journal of Applied and Pure Mathematics

  • 제4권3_4호
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  • Pages.107-122
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  • 2022
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  • 2671-4000(pISSN)
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  • 2636-1612(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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EXISTENCE UNIQUENESS AND STABILITY OF NONLOCAL NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH RANDOM IMPULSES AND POISSON JUMPS

  • CHALISHAJAR, DIMPLEKUMAR (Department of Applied Mathematics, Mallory Hall, Virginia Military Institute) ;
  • RAMKUMAR, K. (Department of Mathematics, PSG College of Arts and Science) ;
  • RAVIKUMAR, K. (Department of Mathematics, PSG College of Arts and Science) ;
  • COX, EOFF (Department of Applied Mathematics, Mallory Hall, Virginia Military Institute)
  • 투고 : 2022.01.22
  • 심사 : 2022.05.24
  • 발행 : 2022.07.30
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초록

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.

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참고문헌

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