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A uniqueness criterion for fractional differential equations with Caputo derivative. (English) Zbl 1268.34008

Summary: We investigate the uniqueness of solutions to an initial value problem associated with a nonlinear fractional differential equation of order \(\alpha \in (0,1)\). The differential operator is of Caputo type whereas the nonlinearity cannot be expressed as a Lipschitz function. Instead, the Riemann-Liouville derivative of this nonlinearity verifies a special inequality.

MSC:

34A08 Fractional ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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