Cauchy problem for fractional evolution equations with Caputo derivative

This paper concerns the abstract nonlocal Cauchy problem of a class of fractional evolution equations with Caputo derivative. A suitable mild solution of evolution equations with Caputo derivative is introduced. In the cases C0 semigroup is compact or noncompact, the existence theorems of mild solutions for the nonlocal Cauchy problem are established by means of fractional calculus, theory of Hausdorff measure of noncompactness and fixed point theorems.

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