Relations between fractional models with three-parameter Mittag-Leffler kernels

Advances in Difference Equations

article

Fernandez, Arran¹  Abdeljawad, Thabet²  Baleanu, Dumitru⁵ 

[1] Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean 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, Cankaya University;Institute of Space Sciences

关键词: Fractional calculus;    Mittag-Leffler functions;    Atangana–Baleanu fractional calculus;    Prabhakar fractional calculus;   

DOI  :  10.1186/s13662-020-02638-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We consider two models of fractional calculus which are defined using three-parameter Mittag-Leffler functions: the Prabhakar definition and a recently defined extension of the Atangana–Baleanu definition. By examining the relationships between the two, we are able to find some new properties of both, as well as of the original Atangana–Baleanu model and its iterated form.

【 授权许可】

CC BY