A Uniqueness Criterion for Fractional Differential Equations With Caputo Derivative

Abstract

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