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

Advances in Difference Equations

article

Abdo, Mohammed S.¹  Abdeljawad, Thabet²  Kucche, Kishor D.⁵  Alqudah, Manar A.⁶  Ali, Saeed M.⁷  Jeelani, Mdi Begum⁸ 

[1] Department of Mathematics, Hodeidah University;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University;Department of Mathematics, Shivaji University;Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University;Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University;Department of Mathematics, Imam Muhammed Ibn Saud Islamic University

关键词: ABC-Caputo pantograph fractional differential equation;    Nonlocal conditions;    Fixed point theorem;    Generalized Gronwall inequality;   

DOI  :  10.1186/s13662-021-03229-8

学科分类：航空航天科学

来源: SpringerOpen

【 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.

【 授权许可】

CC BY