Square-Mean Pseudo Almost Periodic Solutions of Infinite Class in the $α$-Norm under the Light of Measure Theory
Year: 2025
Author: Djendode Mbainadji, Teubé Cyrille Mbainaissem, Issa Zabsonre
African Journal for Industrial and Applied Mathematics, Vol. 1 (2025), Iss. 1 : pp. 74–112
Abstract
This work concerns the existence and uniqueness of square-mean pseudo almost periodic solutions of infinite class in the $\alpha$-norm. The results are obtained using analytic semigroup, fractional $\alpha$-power theory and by making use of Banach fixed point theory. As result, we obtain a generalization of the work of Zabsonre et al. [Partial Differential Equations and Applications: Colloquium in Honor of Hamidou Touré, Springer, 2023] in the deterministic case, without unbounded delay. Our results extend and complement many other important results in the literature. Finally, a concrete example is given to illustrate the application of the main results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ajiam.2025-0005
African Journal for Industrial and Applied Mathematics, Vol. 1 (2025), Iss. 1 : pp. 74–112
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 39
Keywords: Measure theory ergodicity $(\mu ν)$-pseudo almost periodic function partial functional differential equation stochastic process stochastic evolution equation.