Asymptotic Periodicity of Bounded Mild Solutions for Evolution Equations with Non-Densely Defined and Fractional Derivative - Jiabin Zuo; Abdellah Taqbibt; Mohamed Chaib; M’hamed Elomari (Fractal and Fractional)
In the present article, we establish conditions for the asymptotic periodicity of bounded mild solutions in two distinct cases of evolution equations. The first class involves non-densely defined operators, while the second class incorporates densely defined operators with fractional derivatives that generate a semigroup of contractions. Our method integrates the theory of spectral properties of uniformly bounded continuous functions defined on the positive real semi-axis. Additionally, we apply extrapolation theory to evolution equations with non-densely defined operators. To illustrate our main results, we provide a concrete example.