On Hilfer generalized proportional fractional derivative

Autor:	Idris Ahmed, Poom Kumam, Fahd Jarad, Piyachat Borisut, Wachirapong Jirakitpuwapat
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	Existence Proportional fractional derivative Fixed point theorems Nonlocal condition Volterra integral equation Mathematics QA1-939
Zdroj:	Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-18 (2020)
Druh dokumentu:	article
ISSN:	1687-1847
DOI:	10.1186/s13662-020-02792-w
Popis:	Abstract Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann–Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential equation with nonlocal initial condition and show that this equation is equivalent to the Volterra integral equation. In addition, the existence and uniqueness of solutions are proven using fixed point theorems. Furthermore, we offer two examples to clarify the results.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/2b08e2e2f32640df89d97919d46cf414 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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