, Volume 71, Issue 4, pp 635-640
Date: 17 May 2012

A uniqueness criterion for fractional differential equations with Caputo derivative

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We investigate the uniqueness of solutions to an initial value problem associated with a nonlinear fractional differential equation of order α∈(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.

Dedicated to Professor Ravi P. Agarwal.