Existence uniqueness and stability of mild solutions for semilinear ψ-Caputo fractional evolution equations

Autor:	Apassara Suechoei, Parinya Sa Ngiamsunthorn
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	Fractional evolution equation Existence and uniqueness theorems Mild solution Measure of noncompactness Mittag-Leffler–Ulam–Hyers stability Mathematics QA1-939
Zdroj:	Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-28 (2020)
Druh dokumentu:	article
ISSN:	1687-1847
DOI:	10.1186/s13662-020-02570-8
Popis:	Abstract In this paper, we study the local and global existence, and uniqueness of mild solution to initial value problems for fractional semilinear evolution equations with compact and noncompact semigroup in Banach spaces. In particular, we derive the form of fundamental solution in terms of semigroup induced by resolvent and ψ-function from Caputo fractional derivatives. These results generalize previous work where the classical Caputo fractional derivative is considered. Moreover, we prove the Mittag-Leffler–Ulam–Hyers stability result. Finally, we give examples of time-fractional heat equation to illustrate the result.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/62f3a86ca301429db25acae06f6d3985 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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