Nonlinear Dynamics

, Volume 71, Issue 4, pp 635–640

A uniqueness criterion for fractional differential equations with Caputo derivative


  • Dumitru Băleanu
    • Department of Mathematics & Computer ScienceÇankaya University
    • Institute of Space Sciences
    • Faculty of Exact SciencesUniversity of Craiova
  • Donal O’Regan
    • School of Mathematics, Statistics and Applied MathematicsNational University of Ireland
Original Paper

DOI: 10.1007/s11071-012-0449-4

Cite this article as:
Băleanu, D., Mustafa, O.G. & O’Regan, D. Nonlinear Dyn (2013) 71: 635. doi:10.1007/s11071-012-0449-4


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.


Fractional differential equationUniqueness of solutionCaputo differential operatorRiemann–Liouville derivative

Copyright information

© Springer Science+Business Media B.V. 2012