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In this paper, we study a class of fractional semilinear integro-differential equations of order  β  ∈ (1,2] with nonlocal conditions. By using the solution operator, measure of noncompactness and some fixed point theorems, we obtain the existence of local and global mild solutions for the problem. The results presented in this paper improve and generalize many classical results. An example about fractional partial differential equations is given to show the application of our theory.

Local and global existence of mild solutions for a class of semilinear fractional integro-differential equations