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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) {\it A. A. Kilbas, H. M. Srivastava} and {\it J. J. Trujillo}, Theory and applications of fractional differential equations. Amsterdam: Elsevier (2006; Zbl 1092.45003); 2) {\it C. P. Li} and {\it W. H. Deng}, Appl. Math. Comput. 187, No. 2, 777--784 (2007; Zbl 1125.26009)

##### MSC:
 34A12 Initial value problems for ODE, existence, uniqueness, etc. of solutions 34A45 Theoretical approximation of solutions of ODE 26A33 Fractional derivatives and integrals (real functions)
##### Keywords:
uniqueness result; generalized Nagumo condition
Full Text:
##### References:
 [1] Lakshmikantham, V.; Leela, S.; Devi, J. Vasundhara: Theory of fractional dynamic systems. (2009) · 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. (1969) · Zbl 0177.12403 [4] Agarwal, R. P.; Lakshmikantham, V.: Uniqueness and non-uniqueness criteria for ordinary differential equations. (1993) · Zbl 0785.34003