Some Properties of the Functions Representable as Fractional Power Series

Autor:	Ghiocel Groza, Marilena Jianu, Ion Mierluş-Mazilu
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Caputo fractional derivative operator fractional power series fractional analytic function Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 7, p 961 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12070961
Popis:	The α-fractional power moduli series are introduced as a generalization of α-fractional power series and the structural properties of these series are investigated. Using the fractional Taylor’s formula, sufficient conditions for a function to be represented as an α-fractional power moduli series are established. Beyond theoretical formulations, a practical method to represent solutions to boundary value problems for fractional differential equations as α-fractional power series is discussed. Finally, α-analytic functions on an open interval I are defined, and it is shown that a non-constant function is α-analytic on I if and only if 1/α is a positive integer and the function is real analytic on I.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/e1370dc11f214efea336f49b16c85082 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.