Discontinuity, Nonlinearity, and Complexity
Neutral Stochastic Impulsive IntegroDifferential Equations Driven by Fractional Brownian Motion and Brownian Motion with Nonlocal Condition
Discontinuity, Nonlinearity, and Complexity 11(3) (2022) 487500  DOI:10.5890/DNC.2022.09.010
S. Abinaya$^1$, Sayooj Aby Jose$^{2,3}$, Weerawat Sudsutad$^{4,5}$
$^1$ Department of Mathematics, Rathinam College of Arts and Science,
Coimbatore, Tamil Nadu, India
$^2$ Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi630 004, Tamil Nadu, India
$^3$ Department of Mathematics, Alagappa University, Karaikudi630 004, Tamil Nadu, India
$^4$ Department of General Education, Navamindradhiraj University, Bangkok, Thailand
$^5$ Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
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Abstract
In this paper, we present the existence, uniqueness and asymptotic behaviour of mild solution for neutral stochastic impulsive integrodifferential equations driven by fractional Brownian motion and Brownian motion with the Hurst index $H>\frac{1}{2}$ with nonlocal condition. The results are obtained by using Banach fixed point principle in a Hilbert space and the theory of resolvent operator.
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