On Hilfer generalized proportional fractional derivative

被引：0
作者：
Idris Ahmed
Poom Kumam
Fahd Jarad
Piyachat Borisut
Wachirapong Jirakitpuwapat
机构：
[1] King Mongkut’s University of Technology Thonburi (KMUTT),KMUTTFixed Point Research Laboratory, KMUTT
[2] China Medical University,Fixed Point Theory and Applications Research Group (KMUTT
[3] Sule Lamido University,FPTA), Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
[4] Çankaya University,Department of Medical Research, China Medical University Hospital
来源：
Advances in Difference Equations | / 2020卷
关键词：
Existence; Proportional fractional derivative; Fixed point theorems; Nonlocal condition; Volterra integral equation; 26A33; 34A12; 34A43; 34D20;
D O I：
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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.
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