A complex analysis approach to Atangana-Baleanu fractional calculus

被引：39

作者：

Fernandez, Arran ^{[1
]}

机构：

[1] Eastern Mediterranean Univ, Fac Arts & Sci, Dept Math, Via Mersin 10, Gazimagusa, Trnc, Turkey

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 10期

关键词：

analytic continuation; complex analysis; fractional calculus; Mittag-Leffler functions; DERIVATIVES;

D O I：

10.1002/mma.5754

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The standard definition for the Atangana-Baleanu fractional derivative involves an integral transform with a Mittag-Leffler function in the kernel. We show that this integral can be rewritten as a complex contour integral which can be used to provide an analytic continuation of the definition to complex orders of differentiation. We discuss the implications and consequences of this extension, including a more natural formula for the Atangana-Baleanu fractional integral and for iterated Atangana-Baleanu fractional differintegrals.

引用

页码：8070 / 8087

页数：18

共 40 条

[1] Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel [J].