On existence and stability results to a class of boundary value problems under Mittag-Leffler power law

Advances in Difference Equations

article

Ali, Gauhar¹  Shah, Kamal¹  Abdeljawad, Thabet²  Khan, Hasib⁵  Ur Rahman, Ghaus⁶  Khan, Aziz² 

[1] Department of Mathematics, University of Malakand;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, Shaheed Benazir Bhutto University;Department of Mathematics & Statistics, University of Swat

关键词: Boundary conditions;    ABC fractional derivative;    Krasnoselskii fixed point theorem;    Stability theory;   

DOI  :  10.1186/s13662-020-02866-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

Some essential conditions for existence theory and stability analysis to a class of boundary value problems of fractional delay differential equations involving Atangana–Baleanu-Caputo derivative are established. The deserted results are derived by using the Banach contraction and Krasnoselskii’s fixed point theorems. Moreover, different kinds of stability theory including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam-Rassias and generalized Hyers–Ulam–Rassias stability are also developed for the problem under consideration. Appropriate examples are given for illustrative purposes.

【 授权许可】

CC BY