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Nagumo-type uniqueness result for fractional differential equations. (English) Zbl 1177.34003
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) 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, “Remarks on fractional derivatives”, Appl. Math. Comput. 187, No. 2, 777–784 (2007; Zbl 1125.26009).

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
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[1] Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J., Theory of fractional dynamic systems, (2009), Cambridge Academic Publishers Cambridge · Zbl 1188.37002
[2] Agarwal, R.P.; Lakshmikantham, V., Uniqueness and non-uniqueness criteria for ordinary differential equations, (1993), World Scientific Singapore · Zbl 0785.34003
[3] Lakshmikantham, V.; Leela, S., Differential and integral inequalities, vol. I, (1969), Academic Press New York · Zbl 0177.12403
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