Caputo \(\Delta\)-type fractional time-scales Noether theorem of Birkhoffian systems
type: Item
instance of: scholarly article
title: Caputo \(\Delta\)-type fractional time-scales Noether theorem of Birkhoffian systems
author: Xue Tian
author: Yi Zhang
published in: Acta Mechanica
publication date: 2022-11-04T00:00:00Z
review text: Birkhoff systems extend Hamiltonian and Lagrangian formalism, including dissipative systems. They are characterized by invariance of time-dependent symplectic forms on the integral curves. A time-scale is a non-empty closed subset \(\mathbb T\) of \(\mathbb R\), possibly discrete, and represents the ``points'' in time with respect to which the dynamics is analyzed. A calculus is developed for functions \(\mathbb T\rightarrow \mathbb R\). In this article, fractional derivatives and integrals, of Riemann-Liouville and Caputo types, are extended to functions on time-scales. Fractional calculus naturally describes systems with memory, its extension to time-scales allows the inclusion of time-discrete systems in the formalism. Both the above formalisms are employed to define fractional time-scale Birkhoff mechanics. The authors determine Noether-type theorems for this extended Birkhoff mechanics, in particular for Hamiltonian and Lagrangian systems. The Hojman-Urrutia model is studied as an example.
reviewed by: Giovanni Rastelli
Mathematics Subject Classification ID: 70H33
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 7612090
zbMATH Keywords: fractional calculus
zbMATH Keywords: Birkhoff mechanics
zbMATH Keywords: time-scales
zbMATH Keywords: Noether theorems
MaRDI profile type: Publication
full work available at URL: s00707-022-03338-9
OpenAlex ID: W4297903129
Wikidata QID: Q115236529
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DOI: 10.1007/S00707-022-03338-9
description: scientific article; zbMATH DE number 7612090