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Fractional differential equations with a Krasnoselskii-Krein type condition. (English) Zbl 1181.34008
Summary: We consider an initial value problem for a fractional differential equation of Caputo type. The convergence of the Picard successive approximations is established by first showing that the Caputo derivatives of these approximations converge.

34A08Fractional differential equations
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
Full Text: DOI
[1] Agarwal, R. P.; Lakshmikantham, V.: Uniqueness and nonuniqueness criteria for ordinary differential equations. (1993) · Zbl 0785.34003
[2] Kooi, O.: The method of successive approximations and a uniqueness theorem of Krasnoselskii--Krein in the theory of differential equations. Nederi. akad. Wetensch, proc. Ser. A61; indag. Math. 20, 322-327 (1958)
[3] Krasnoselskii, M. A.; Krein, S. G.: On a class of uniqueness theorems for the equation y’=$f(x,y)$, usphe. Mat. nauk (N.S). 11, No. 1, 209-213 (1956)
[4] Lakshmikantham, V.; Leela, S.; Devi, J. Vasundhara: Theory of fractional dynamical systems. (2009) · Zbl 1188.37002
[5] Lakshmikantham, V.; Leela, S.: Krasnoselskii--Krein type uniqueness result for fractional differential equations. Nonlinear anal. TMA 71, No. 7--8, 3421-3424 (2009) · Zbl 1177.34004