Standard Methods in Fractional Variational Calculus

  • Agnieszka B. Malinowska
  • Tatiana Odzijewicz
  • Delfim F. M. Torres
Chapter
First Online:
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

We investigate the problem of finding an admissible function giving a minimum value to an integral functional that depends on an unknown function (or functions) of one or several variables and its generalized fractional derivatives and/or generalized fractional integrals. The appropriate Euler–Lagrange equations and natural boundary conditions are obtained. Moreover, Noether-type theorems (without transformation of time) are presented.

Keywords

Generalized fractional calculus of variations Fractional integration by parts Isoperimetric problems Natural boundary conditions Fractional Euler–Lagrange equations Fractional Noether’s theorem 
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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Agnieszka B. Malinowska
    • 1
  • Tatiana Odzijewicz
    • 2
  • Delfim F. M. Torres
    • 3
  1. 1.Faculty of Computer ScienceBialystok University of TechnologyBiałystokPoland
  2. 2.Department of Mathematics and Mathematical EconomicsWarsaw School of EconomicsWarsawPoland
  3. 3.Department of MathematicsUniversity of AveiroAveiroPortugal

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