Perturbation theory for fractional evolution equations in a Banach space

A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. We study fractional evolution equations of order α∈(1,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (1,2)$$\end{document} associated with the infinitesimal generator of an operator fractional cosine (sine) function generated by bounded time-dependent perturbations in a Banach space. We show that the fractional abstract Cauchy problem associated with the infinitesimal generator A of a strongly continuous fractional cosine (sine) function remains uniformly well-posed under bounded time-dependent perturbation of A. We also provide some necessary special cases by using the Laplace transform of the generators of the given operator families.