Nonlinear Dynamics

, Volume 52, Issue 4, pp 331–335 | Cite as

On exact solutions of a class of fractional Euler–Lagrange equations

  • Dumitru BaleanuEmail author
  • Juan J. Trujillo
Original Paper


In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian L(x(t), where a c D t α x(t)) and 0<α<1, such that the following is the corresponding Euler–Lagrange
At last, exact solutions for some Euler–Lagrange equations are presented. In particular, we consider the following equations
$$\lefteqn{{}_{t}D_{b}^{\alpha}\bigl({}_{a}^{c}D_{t}^{\alpha}x(t)\bigr)=\lambda x(t)\quad (\lambda\in R),}$$
where g(t) and f(t) are suitable functions.


Fractional calculus Differential equations of fractional order Fractional variational calculus 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Sciences, Faculty of Arts and SciencesÇankaya UniversityAnkaraTurkey
  2. 2.Departamento de Análisis MatemáticoUniversity of La LagunaLa LagunaSpain

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