Abstract Differential Equations and Caputo Fractional Derivative

Abstract

In this work I consider the abstract Cauchy problems with Caputo fractional time derivative of order $\alpha \in (0,1]$, and discuss the continuity of the respective solutions regarding the parameter $\alpha$. I also present a study about the continuity of the Mittag-Leffler families of operators (for $\alpha \in (0,1]$), induced by sectorial operators.