Volume 1, Issue 1
Square-Mean Pseudo Almost Periodic Solutions of Infinite Class in the $α$-Norm under the Light of Measure Theory

Djendode Mbainadji, Teubé Cyrille Mbainaissem & Issa Zabsonre

Afr. J. Ind. Appl. Math., 1 (2025), pp. 74-112.

Published online: 2025-06

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  • 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 a 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.

  • AMS Subject Headings

34K14, 35B15, 34G10, 60J65

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COPYRIGHT: © Global Science Press

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@Article{AJIAM-1-74, author = {Mbainadji , DjendodeMbainaissem , Teubé Cyrille and Zabsonre , Issa}, title = {Square-Mean Pseudo Almost Periodic Solutions of Infinite Class in the $α$-Norm under the Light of Measure Theory}, journal = {African Journal for Industrial and Applied Mathematics}, year = {2025}, volume = {1}, number = {1}, pages = {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 a 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.

}, issn = {3105-3289}, doi = {https://doi.org/10.4208/ajiam.2025-0005}, url = {http://global-sci.org/intro/article_detail/ajiam/24223.html} }
TY - JOUR T1 - Square-Mean Pseudo Almost Periodic Solutions of Infinite Class in the $α$-Norm under the Light of Measure Theory AU - Mbainadji , Djendode AU - Mbainaissem , Teubé Cyrille AU - Zabsonre , Issa JO - African Journal for Industrial and Applied Mathematics VL - 1 SP - 74 EP - 112 PY - 2025 DA - 2025/06 SN - 1 DO - http://doi.org/10.4208/ajiam.2025-0005 UR - https://global-sci.org/intro/article_detail/ajiam/24223.html KW - Measure theory, ergodicity, $(\mu, ν)$-pseudo almost periodic function, partial functional differential equation, stochastic process, stochastic evolution equation. AB -

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 a 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.

Mbainadji , DjendodeMbainaissem , Teubé Cyrille and Zabsonre , Issa. (2025). Square-Mean Pseudo Almost Periodic Solutions of Infinite Class in the $α$-Norm under the Light of Measure Theory. African Journal for Industrial and Applied Mathematics. 1 (1). 74-112. doi:10.4208/ajiam.2025-0005
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