General Fractional Noether Theorem and Non-Holonomic Action Principle

Tarasov, V.E.

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.

Автор: Tarasov Vasily E.
Журнал: Mathematics
Том: 11
Номер: 20
Год издания: 2023
Издательство: MDPI
Местоположение издательства: Basel, Switzerland
Первая страница: 1
Последняя страница: 35
Номер статьи: 4400
DOI: 10.3390/math11204400
Аннотация: Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows us to take into account a wide class of nonlocalities in space and time compared to the usual fractional calculus. The use of non-holonomic variation equations allows us to consider field equations and equations of motion for a wide class of irreversible processes, dissipative and open systems, non-Lagrangian and non-Hamiltonian field theories and systems. In addition, the proposed GF action principle and the GF Noether theorem are generalized to equations containing general fractional integrals (GFI) in addition to general fractional derivatives (GFD). Examples of field equations with GFDs and GFIs are suggested. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for general fractional non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory.
Добавил в систему: Тарасов Василий Евгеньевич

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