Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels

Advances in Difference Equations

Thabet Abdeljawad¹  Dumitru Baleanu² 

[1] Department of Mathematics and Physical Sciences, Prince Sultan University, Riyadh, Saudi Arabia;Department of Mathematics, Çankaya University, Ankara, Turkey

关键词: discrete fractional derivative;    modified Mittag-Leffler function;    discrete Mittag-Leffler function;    discrete nabla Laplace transform;    convolution;    discrete \(ABR\) fractional derivative;   

DOI  :  10.1186/s13662-016-0949-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this manuscript we propose the discrete versions for the recently introduced fractional derivatives with nonsingular Mittag-Leffler function. The properties of such fractional differences are studied and the discrete integration by parts formulas are proved. Then a discrete variational problem is considered with an illustrative example. Finally, some more tools for these derivatives and their discrete versions have been obtained.

【 授权许可】

CC BY