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By means of a Laplace transform and its inverse transform, we obtain a correct equivalent integral equation for some kind of nonlocal abstract differential equations (fractional order) on the right half-axis. Based on it, the existence result is established by Knaster's theorem, and the uniqueness of the mild solution is obtained using the Banach contraction principle. MSC: Primary 26A33; 34A08; secondary 34G20doi:10.1186/s13661-018-1095-7 fatcat:eyqelqsikbhxrabh26zka6incm