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Zbl 1177.34004
Lakshmikantham, V.; Leela, S.
A Krasnoselskii-Krein-type uniqueness result for fractional differential equations. (English)
[J] Nonlinear Anal., Theory Methods Appl. 71, No. 7-8, A, 3421-3424 (2009). ISSN 0362-546X

The Krasnoselskii-Krein-type uniqueness result and the convergence of successive approximations is extended to fractional differential equations. \par 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)
[Li Changpin (Logan)]

MSC 2000:: *34A12 Initial value problems for ODE
34A45 Theoretical approximation of solutions of ODE
26A33 Fractional derivatives and integrals (real functions)

Keywords: uniqueness result; generalized Nagumo condition

Citations: Zbl 1092.45003; Zbl 1125.26009

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