Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundar...

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Veröffentlicht in:Abstract and Applied Analysis 2012-01, Vol.2012 (2012), p.199-222-713
Hauptverfasser: Odzijewicz, Tatiana, Malinowska, Agnieszka B., Torres, Delfim F. M.
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Calculus
Calculus of variations
Derivatives
Integrals
Isoperimetric problem
Mathematical analysis
Mathematics
Optimization
Optimization and Control
Studies
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Zusammenfassung:We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to physics discussed.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/871912