The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative

Abstract

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.

Accepted (19 February 2010) for publication in Computers and Mathematics with Applications

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• Generalized fractional calculus with applications to the calculus of variations
• Numerical Approximations of Fractional Derivatives with Applications
• Fractional variational problems depending on indefinite integrals
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
• Fractional variational calculus of variable order
• Approximation of fractional integrals by means of derivatives
• Fractional variational calculus for nondifferentiable functions
• Multiobjective fractional variational calculus in terms of a combined Caputo derivative
• Fractional Euler-Lagrange differential equations via Caputo derivatives
• Composition Functionals in Fractional Calculus of Variations
• Lyapunov-type inequality for a fractional boundary value problem with natural conditions
• Generalized Transversality Conditions in Fractional Calculus of Variations
• Isoperimetric problems of the calculus of variations with fractional derivatives
• Fractional Calculus on Time Scales
• Fractional variational calculus in terms of a combined Caputo derivative
• Calculus of Variations with Classical and Fractional Derivatives
• Fractional Calculus of Variations for Double Integrals
• Numerical Approximations to Fractional Problems of the Calculus of Variations and Optimal Control
• Variational Problems Involving a Caputo-Type Fractional Derivative
• Optimality conditions for fractional variational problems with free terminal time
• Generalized Fuzzy Euler-Lagrange equations and transversality conditions
• Fractional variational problems depending on indefinite integrals and with delay