On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

被引：32

作者：

Abdo, Mohammed S. ^{[1
]}

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

Ali, Saeed M. ^{[5
]}

Shah, Kamal ^{[6
]}

机构：

[1] Hodeidah Univ, Dept Math, Al Hodeidah, Yemen

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

[3] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

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

[5] Imam Abdulrahman Bin Faisal Univ, Coll Engn, Dept Basic Engn Sci, POB 1982, Dammam 34151, Saudi Arabia

[6] Univ Malakand, Dept Math, Chakdara Dir Lower, Khyber Pakhtunk, Pakistan

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2021年 / 2021卷 / 01期

关键词：

Implicit fractional differential equations; Atangana-Baleanu-Caputo fractional derivative; Integral conditions; Fixed point theorems; 34A08; 34A12; 47H10; EVOLUTION-EQUATIONS; PARAMETER; MODEL;

D O I：

10.1186/s13662-020-03196-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana-Baleanu-Caputo fractional derivatives of orders 0<<theta><= 1 and 1<<theta><= 2. We structure the equivalent fractional integral equations of the proposed problems. Further, the existence and uniqueness theorems are proved with the aid of fixed point theorems of Krasnoselskii and Banach. Lastly, the paper includes pertinent examples to justify the validity of the results.

引用

页数：21

共 56 条

[1] Solutions of boundary value problems on extended-Branciari b-distance [J].