文章基本信息

标题：On Hilfer generalized proportional fractional derivative
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作者：Idris Ahmed ; Poom Kumam ; Fahd Jarad 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-18
DOI：10.1186/s13662-020-02792-w
出版社：Hindawi Publishing Corporation
摘要：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.
关键词：Existence;Proportional fractional derivative;Fixed point theorems;Nonlocal condition;Volterra integral equation;