Fractional differential equations with a Krasnoselskii-Krein typecondition

摘要

We consider an initial value problem for a fractional differential equation of Caputotype. The convergence of the Picard successive approximations is established by firstshowing that the Caputo derivatives of these approximations converge. The methodutilized, originally introduced in [0. Kooi, The method of successive approximations and auniqueness theorem of Krasnoselskii-Krein in the theory of differential equations, Nederi.Akad. Wetensch, Proc. Ser. A61; Indag. Math. 20 (1958) 322-327], is interesting in itself.