Composition Functionals in Fractional Calculus of Variations

Abstract

We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. As an application, we get optimality conditions for the product and the quotient of fractional variational functionals.

This is a preprint of a paper whose final form has appeared in Commun. Frac. Calc. 1 (2010) 32-40

References in corpus (6)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Calculus of variations with fractional derivatives and fractional integrals
• Fractional Noether's theorem in the Riesz-Caputo sense
• Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order $(\alpha ,\beta )$
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Cited by in corpus (3)

• Fractional Variational Iteration Method for Fractional Nonlinear Differential Equations
• Fractional variational calculus for nondifferentiable functions
• Fractional Calculus of Variations for Double Integrals