Nonlinear Dynamics

, Volume 71, Issue 4, pp 635–640

A uniqueness criterion for fractional differential equations with Caputo derivative

  • Dumitru Băleanu
  • Octavian G. Mustafa
  • Donal O’Regan
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

Authors and Affiliations

  • Dumitru Băleanu
    • 1
    • 2
  • Octavian G. Mustafa
    • 3
  • Donal O’Regan
    • 4
  1. 1.Department of Mathematics & Computer ScienceÇankaya UniversityBalgatTurkey
  2. 2.Institute of Space SciencesMăgureleRomania
  3. 3.Faculty of Exact SciencesUniversity of CraiovaCraiovaRomania
  4. 4.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland