Fractional Euler-Lagrange differential equations via Caputo derivatives

Abstract

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.

This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in press

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• Fractional variational problems depending on indefinite integrals
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
• Existence of Minimizers for Fractional Variational Problems Containing Caputo Derivatives
• The DuBois-Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler-Lagrange Equation Involving only Derivatives of Caputo
• A Generalized Fractional Calculus of Variations
• Variable Order Fractional Variational Calculus for Double Integrals
• Weighted Generalized Fractional Integration by Parts and the Euler-Lagrange Equation
• Complementary Fractional Dimensional Order of Nyquist Sinc Sequences for Time Division Multiplexing
• A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems