P-mean \((\mu_1, \mu_2)\)-pseudo almost periodic processes and application to integro-differential stochastic evolution equations. (English) Zbl 1534.34078
Summary: 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.
MSC:
| 34K50 | Stochastic functional-differential equations |
| 34K14 | Almost and pseudo-almost periodic solutions to functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
Keywords:
p-mean \((\mu_1, \mu_2)\)-pseudo almost periodic process; fixed-point theorem; integro-differential stochastic evolution equation; existence; stabilityReferences:
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