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A uniqueness criterion for fractional differential equations with Caputo derivative

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Abstract

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.

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Acknowledgement

The work of the second author has been supported by a grant of the Romanian National Authority for Scientific Research, CNCS—UEFISCDI, project number PN-II-ID-PCE-2011-3-0257.

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Authors and Affiliations

  1. Department of Mathematics & Computer Science, Çankaya University, Ögretmenler Cad. 14, 06530, Balgat, Ankara, Turkey

    Dumitru Băleanu

  2. Institute of Space Sciences, Măgurele, Bucureşti, Romania

    Dumitru Băleanu

  3. Faculty of Exact Sciences, University of Craiova, A.I. Cuza 13, 200534, Craiova, Romania

    Octavian G. Mustafa

  4. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Dumitru Băleanu
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  2. Octavian G. Mustafa
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  3. Donal O’Regan
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Corresponding author

Correspondence to Octavian G. Mustafa.

Additional information

Dedicated to Professor Ravi P. Agarwal.

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Băleanu, D., Mustafa, O.G. & O’Regan, D. A uniqueness criterion for fractional differential equations with Caputo derivative. Nonlinear Dyn 71, 635–640 (2013). https://doi.org/10.1007/s11071-012-0449-4

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  • DOI: https://doi.org/10.1007/s11071-012-0449-4

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