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, 2025)
This work concerns the existence and uniqueness of square-mean pseudoalmost periodic solutions of infinite class in the $α$-norm. The results are obtainedusing analytic semigroup, fractional $α$-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 Honorof Hamidou Touré, Springer, 2023] in the deterministic case, without unboundeddelay. Our results extend and complement many other important results in the literature. Finally, a concrete example is given to illustrate the application of the mainresults.
Keywords: Measure theory; ergodicity; $(μ; ν)$-pseudo almost periodic function; partial functional differential equation; stochastic process; stochastic evolution equation.