The Krasnoselskii-Krein-type uniqueness result and the convergence of successive approximations is extended to fractional differential equations.
Reviewer’s remark: I think the initial value condition of equation (1) should be replaced by , or some other equivalent forms. The reason why the initial value condition should be chosen like this can be found from the following references: 1) A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations. Amsterdam: Elsevier (2006; Zbl 1092.45003); 2) C. P. Li and W. H. Deng, Appl. Math. Comput. 187, No. 2, 777–784 (2007; Zbl 1125.26009)