Nonlinear Dynamics

, Volume 69, Issue 3, pp 977–982

Fractional Euler–Lagrange equations revisited

Original Paper


This paper presents the necessary and sufficient optimality conditions for the Euler–Lagrange fractional equations of fractional variational problems with determining in which spaces the functional must exist where the functional contains right and left fractional derivatives in the Riemann–Liouville sense and the upper bound of integration less than the upper bound of the interval of the fractional derivative. In order to illustrate our results, one example is presented.


Fractional integral Fractional derivative Fractional calculus of variations Lipschitz spaces 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.College of Science in ZulfiMajmaah UniversityRiyadhSaudi Arabia
  2. 2.Faculty of ScienceZagazig UniversityZagazigEgypt
  3. 3.Department of Mathematics and Computer ScienceÇankaya UniversityAnkaraTurkey
  4. 4.Institute of Space SciencesMagurele-BucharestRomania

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