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Fractional Calculus for Non-discrete Signed Measuresстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Колокольцов В.Н., Шишкина Элина Леонидовна
- Журнал: Mathematics
- Том: 12
- Год издания: 2024
- Издательство: MDPI
- Местоположение издательства: Basel, Switzerland
- Номер статьи: 2804
- DOI: 10.3390/math12182804
- Аннотация: In this paper, we suggest a first-ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann–Stieltjes integral with a signed measure, using semigroup theory. The main result is a theorem that provides the exact form of a semigroup for the Riemann–Stieltjes integral with a measure having a countable number of extrema. This article provides examples of semigroups based on integral operators with signed measures and discusses the fractional powers of differential operators with partial derivatives.
- Добавил в систему: Колокольцов Василий Никитич