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Zbl 1177.34003
Lakshmikantham, V.; Leela, S.
Nagumo-type uniqueness result for fractional differential equations. (English)
[J] Nonlinear Anal., Theory Methods Appl. 71, No. 7-8, A, 2886-2889 (2009). ISSN 0362-546X

The authors consider the Nagumo-type uniqueness result for a fractional differential equation with Riemann-Liouville derivative. I think the initial value condition of equation (2.1) 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}, ``Remarks on fractional derivatives", Appl. Math. Comput. 187, No.~2, 777--784 (2007; Zbl 1125.26009).
[Li Changpin (Logan)]

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

Keywords: fractional differential equations; Riemann-Liouville derivative; uniqueness

Citations: Zbl 1092.45003; Zbl 1125.26009

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