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

Advances in Difference Equations

article

Abdo, Mohammed S.¹  Abdeljawad, Thabet²  Ali, Saeed M.⁵  Shah, Kamal⁶ 

[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 Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University;Department of Mathematics, University of Malakand

关键词: Implicit fractional differential equations;    Atangana–Baleanu–Caputo fractional derivative;    Integral conditions;    Fixed point theorems;   

DOI  :  10.1186/s13662-020-03196-6

学科分类：航空航天科学

来源: SpringerOpen

【 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$0<\vartheta \leq 1$ and$1<\vartheta \leq 2$ . 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.

【 授权许可】

CC BY