General fractional calculus in multi-dimensional space: Riesz form

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: 20 февраля 2024 г.

Автор: Tarasov Vasily E.
Журнал: Mathematics
Том: 11
Номер: 7
Год издания: 2023
Издательство: MDPI
Местоположение издательства: Basel, Switzerland
Номер статьи: 1651
DOI: 10.3390/math11071651
Аннотация: An extension of the general fractional calculus (GFC) is proposed as a generalization of the Riesz fractional calculus, which was suggested by Marsel Riesz in 1949. The proposed Riesz form of GFC can be considered as an extension GFC from the positive real line and the Laplace convolution to the m-dimensional Euclidean space and the Fourier convolution. To formulate the general fractional calculus in the Riesz form, the Luchko approach to construction of the GFC, which was suggested by Yuri Luchko in 2021, is used. The general fractional integrals and derivatives are defined as convolution-type operators. In these definitions the Fourier convolution on m-dimensional Euclidean space is used instead of the Laplace convolution on positive semi-axis. Some properties of these general fractional operators are described. The general fractional analogs of first and second fundamental theorems of fractional calculus are proved. The fractional calculus of the Riesz potential and the fractional Laplacian of the Riesz form are special cases of proposed general fractional calculus of the Riesz form.
Добавил в систему: Тарасов Василий Евгеньевич

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General fractional calculus in multi-dimensional space: Riesz formстатья

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