... 0,T,u0A−10guu0, in Banach spaces, where T>0, 0 <q<1. New results are obtained byusing Sadovskii’s fixed point theorem and the Banach contraction mapping principle. An exampleis also given.1. IntroductionDuring ... IntroductionDuring the past decades, the fractional differential equations have been proved to be valuabletools in the investigation of many phenomena in engineering and physics; they attractedmany researchers ... studied in, for example, 6, 7, 10–20,andthenonlocal C auchy problem was considered in, for example, 2, 5, 18, 21–26. In this paper, we consider the following nonlocal Cauchy problem for nonautonomousfractional...