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 - <p style="text-align: justify;">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.</p>