Electron. J. Differential Equations, Vol. 2024 (2024), No. 24, pp. 1-26.

P-mean (mu1,mu2)-pseudo almost periodic processes and application to integro-differential stochastic evolution equations

Moez Ayachi, Syed Abbas

In this article, we investigate the existence and stability of p-mean \((\mu_1,\mu_2)\)-pseudo almost periodic solutions for a class of non-autonomous integro-differential stochastic evolution equations in a real separable Hilbert space. Using stochastic analysis techniques and the contraction mapping principle, we prove the existence and uniqueness of p-mean \((\mu_1,\mu_2)\)-pseudo almost periodic solutions. We also provide sufficient conditions for the stability of these solutions. Finally, we present three examples with numerical simulations to illustrate the significance of the main findings.

Submitted June 21, 2023 Published March 14, 2024.
Math Subject Classifications: 34K50, 34K14, 34K20.
Key Words: P-mean (mu1,mu2)-pseudo almost periodic process; fixed-point theorem; integro-differential stochastic evolution equation; existence; stability.
DOI: 10.58997/ejde.2023.24

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Moez Ayachi
Laboratory of Mathematics and Applications (LR17ES11)
Faculty of Sciences of Gabes
University of Gabes, Gabes 6072, Tunisia
email: Moez.Ayachi@fsg.rnu.tn
Syed Abbas
School of Mathematical and Statistical Sciences
Indian Institute of Technology Mandi
Mandi, H.P., 175005, India
email: abbas@iitmandi.ac.in

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