Fractional variational problems depending on indefinite integrals

Abstract

We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and natural boundary conditions, which provide a generalization of previous results found in the literature. Isoperimetric problems, problems with holonomic constraints and depending on higher-order Caputo derivatives, as well as fractional Lagrange problems, are considered.

Submitted 29-Dec-2010; revised 14-Feb-2011; accepted 16-Feb-2011; for publication in Nonlinear Analysis Series A: Theory, Methods & Applications

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Cited by in corpus (17)

• Generalized fractional calculus with applications to the calculus of variations
• Discrete Direct Methods in the Fractional Calculus of Variations
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
• Approximation of fractional integrals by means of derivatives
• Towards a combined fractional mechanics and quantization
• A numerical scheme to solve fractional optimal control problems
• Existence of Minimizers for Fractional Variational Problems Containing Caputo Derivatives
• The action principle for dissipative systems
• Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense
• The DuBois-Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler-Lagrange Equation Involving only Derivatives of Caputo
• Generalized Transversality Conditions in Fractional Calculus of Variations
• The Legendre Condition of the Fractional Calculus of Variations
• Fractional Calculus on Time Scales
• Variable Order Fractional Variational Calculus for Double Integrals
• Fractional Bosonic Strings
• Calculus of Variations with Classical and Fractional Derivatives
• Numerical Approximations to Fractional Problems of the Calculus of Variations and Optimal Control