Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 24, pp. 1-26.

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

Authors: Moez Ayachi (Univ. of Gabes, Gabes, Tunisia)
         Syed Abbas (Indian Institute of Tech., Mandi, HP, India)

Abstract:
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.