Journal of Applied Nonlinear Dynamics 11(4) (2022) 863--873 | DOI:10.5890/JAND.2022.12.007

K. Ramkumar, K. Ravikumar, A. Anguraj

Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 014, India

Abstract

In this manuscript, we establish the existence and exponential stability of neutral stochastic integrodifferential equation driven by fractional Brownian motion and Poisson jumps in a Hilbert space. We prove an existence results and establishes some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point principle and the theory of resolvent operator developed by Grimmer (1982). An example illustrates the potential benefits of these results.

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