On nonlinear pantograph fractional differential equations with Atangana-Baleanu-Caputo derivative

被引：37

作者：

Abdo, Mohammed S. ^{[1
]}

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

Kucche, Kishor D. ^{[5
]}

Alqudah, Manar A. ^{[6
]}

Ali, Saeed M. ^{[7
]}

Jeelani, Mdi Begum ^{[3
,8
]}

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] Shivaji Univ, Dept Math, Kolhapur 416004, Maharashtra, India

[6] Princess Nourah Bint Abdulrahman Univ, Dept Math Sci, Riyadh, Saudi Arabia

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

[8] Imam Muhammed Ibn Saud Islamic Univ, Dept Math, Riyadh, Saudi Arabia

来源：

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

关键词：

ABC-Caputo pantograph fractional differential equation; Nonlocal conditions; Fixed point theorem; Generalized Gronwall inequality; 34A08; 34D20; 97M70; 34A12; EXISTENCE;

D O I：

10.1186/s13662-021-03229-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we obtain sufficient conditions for the existence and uniqueness results of the pantograph fractional differential equations (FDEs) with nonlocal conditions involving Atangana-Baleanu-Caputo (ABC) derivative operator with fractional orders. Our approach is based on the reduction of FDEs to fractional integral equations and on some fixed point theorems such as Banach's contraction principle and the fixed point theorem of Krasnoselskii. Further, Gronwall's inequality in the frame of the Atangana-Baleanu fractional integral operator is applied to develop adequate results for different kinds of Ulam-Hyers stabilities. Lastly, the paper includes an example to substantiate the validity of the results.

引用

页数：17

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