Afr. J. Ind. Appl. Math., 1 (2025), pp. 74-112.
Published online: 2025-06
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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} }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.