Fractional Calculus for Non-Discrete Signed Measures

Autor:	Vassili N. Kolokoltsov, Elina L. Shishkina
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	general fractional calculus fractional integral with signed measure fractional power of first-order partial differential operator quantum mechanic fractional Poisson brackets fractional Heisenberg brackets Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 18, p 2804 (2024)
Druh dokumentu:	article
ISSN:	2227-7390 03618404
DOI:	10.3390/math12182804
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/59b5f5b03618404cbbf43f499de09975 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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