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