Asymptotically almost periodic solutions for some partial differential inclusions in \(\alpha \)-norm

In this paper, we focus on investigating the existence of mild solutions and asymptotically almost periodic mild solutions for a class of partial differential inclusions. These inclusions involve a forcing multivalued function that relies on implicit spatial derivatives of the state variable. We introduce a novel approach to simplify the complexities associated with singularities when taking the \(\alpha \) $\alpha$ -norm.