On Fractional Variational Problems which Admit Local Transformations

2012/03/09 by Agnieszka B. Malinowska, Malinowska, Agnieszka B. · 1 citation
Engineering · Mathematics · #Composite Structure Analysis and Optimization #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1203.2102

This is a preprint of a paper whose final and definite form will be published in: Journal of Vibration and Control. arXiv admin note: text overlap with arXiv:1108.3493 by other author

arxiv created 2012/03/09 · openalex publication_date 2012/03/09 · arxiv updated 2012/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the second Noether theorem to fractional variational problems which are invariant under infinitesimal transformations that depend upon r arbitrary functions and their fractional derivatives in the sense of Caputo. Our main result is illustrated using the fractional Lagrangian density of the electromagnetic field.

Citations

• Gauge Invariant Fractional Electromagnetic Fields

Cited by

• The DuBois-Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler-Lagrange Equation Involving only Derivatives of Caputo

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