... 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 ... getgu≤1λu,αgD≤1λαD4.6 for any D ⊂ X. Then the above equation 4.1 can be written in the abstract form as 1.1.On the other hand,ft,Kut,Hutξ≤tnnK1ut, ... show that there exists m ∈ N such that FBm ⊂ Bm.Suppose the contrary, that for every m ∈ N,thereexistsum∈ Bmand tm∈ I,suchthatFumtm >m. However, on the other handft,K1umt,K2umt,...