Journal of Applied Nonlinear Dynamics 13(2) (2024) 405--416 | DOI:10.5890/JAND.2024.06.014

S. Varshini$^1$, K. Banupriya$^2$, K. Ramkumar$^2$, K. Ravikumar$^2$

$^1$ Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore – 641202, India

$^2$ Department of Mathematics, PSG College of Arts & Science, Coimbatore, 641014, India

Abstract

This article concentrates in analysing a stochastic neutral integro-differential equations with infinite delay, fractional Brownian motion and Poisson jumps in concrete-fading memory phase space $\mathcal{C}_{\mu}$. We introduce sufficient conditions to acquire existence and uniqueness of mild solution in the $p$th moment by using stochastic analysis technique, successive approximation method and Grimmer's resolvent operator theory. Moreover, in the later part mean square exponential stability and almost surely exponential stability of solutions are investigated. Finally, an example is provided to validate the obtained results.

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