Fractional Euler–Lagrange Differential Equations via Caputo Derivatives

  • Ricardo AlmeidaEmail author
  • Agnieszka B. Malinowska
  • Delfim F. M. Torres


We review some of the recent results of the fractional variational calculus. Necessary optimality conditions of Euler–Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.



Work supported by FEDER funds through COMPETE — Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveir) and the Portuguese Foundation for Science and Technology (“FCT — Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/Ul4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690. Agnieszka Malinowska is also supported by Białystok University of Technology grant S/WI/2/2011.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Ricardo Almeida
    • 1
    Email author
  • Agnieszka B. Malinowska
    • 2
  • Delfim F. M. Torres
    • 1
  1. 1.Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Faculty of Computer ScienceBiałystok University of TechnologyBiałystokPoland

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