Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 347–354 | Cite as

Generalized variational problems and Birkhoff equations

  • Hong-Bin Zhang
  • Hai-Bo Chen
Original Paper


In this paper, we present a generalized fractional Birkhoffian equations in terms of Agrawal’s new operators. By choosing different parameter set, we may obtain six kinds of Birkhoffian equations in terms of Riemann–Liouville, Caputo, Riesz and Riesz–Caputo fractional derivatives, respectively. The previous results can be obtained as a special case.


Birkhoffian equation Calculus of variations Fractional derivatives 



We express our sincere thinks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 10872037, 11742063 and the Natural Science Foundation of Anhui Province under Grant No. 070416226.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of PhysicsAnhui Chaohu UniversityChaohuPeople’s Republic of China

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