More properties of the proportional fractional integrals and derivatives of a function with respect to another function

被引：60

作者：

Jarad, Fahd ^{[1
]}

Abdeljawad, Thabet ^{[2
,3
,4
]}

Rashid, Saima ^{[5
]}

Hammouch, Zakia ^{[6
]}

机构：

[1] Cankaya Univ, Dept Math, Ankara, Turkey

[2] Prince Sultan Univ, Dept Math & Gen Sci, Riyadh, Saudi Arabia

[3] China Med Univ, Dept Med Res, Taichung, Taiwan

[4] Asia Univ, Dept Comp Sci & Informat Engn, Taichung, Taiwan

[5] Govt Coll Univ, Dept Math, Faisalabad, Pakistan

[6] Univ Moulay Ismail, FST Errachidia, Dept Math, Equipe E3MI, Errachidia, Morocco

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

General proportional integrals; General proportional derivatives; General Caputo proportional derivative;

D O I：

10.1186/s13662-020-02767-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann-Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators.

引用

页数：16

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