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A Krasnoselskii-Krein-type uniqueness result for fractional differential equations. (English) Zbl 1177.34004
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 \(x(t)(t-t_0)|_{t=t_0}=x^0\), 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)

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
Full Text: DOI
[1] Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J., Theory of fractional dynamic systems, (2009), Cambridge Academic Publishers Cambridge · Zbl 1188.37002
[2] V. Lakshmikantham, S. Leela, Nagumo-type uniqueness result for fractional differential equations, J. Nonlinear Anal., in press (doi:10.1016/j.na.2009.01.169) · Zbl 1177.34003
[3] Lakshmikantham, V.; Leela, S., Differential and integral inequalities, vol. I, (1969), Academic Press New York · Zbl 0177.12403
[4] Agarwal, R.P.; Lakshmikantham, V., Uniqueness and non-uniqueness criteria for ordinary differential equations, (1993), World Scientific Singapore · Zbl 0785.34003
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