Bhaskar, T. Gnana; Lakshmikantham, V.; Leela, S. Fractional differential equations with a Krasnoselskii-Krein type condition. (English) Zbl 1181.34008 Nonlinear Anal., Hybrid Syst. 3, No. 4, 734-737 (2009). 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. Cited in 25 Documents MSC: 34A08 Fractional ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations Keywords:fractional differential equations; Caputo derivative; Krasnoselskii-Krein type conditions × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Agarwal, R. P.; Lakshmikantham, V., Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations (1993), World Scientific: World Scientific Singapore · 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) · Zbl 0084.28402 [3] Krasnoselskii, M. A.; Krein, S. G., On a class of uniqueness theorems for the equation \(y^\prime = f(x, y)\), Usphe. Mat. Nauk (N.S), 11, 1, 209-213 (1956), (Russian: Math. Reviews 18, p. 38) [4] Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J., Theory of Fractional Dynamical Systems (2009), Cambridge Academic Publishers: Cambridge Academic Publishers Cambridge · Zbl 1188.37002 [5] Lakshmikantham, V.; Leela, S., Krasnoselskii-Krein type uniqueness result for fractional differential equations, Nonlinear Anal. TMA, 71, 7-8, 3421-3424 (2009) · Zbl 1177.34004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.