Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels

作者：Abdeljawad, Thabet; Baleanu, Dumitru^*

来源：Advances in Difference Equations, 2016, 2016(1): 232.

DOI：10.1186/s13662-016-0949-5

• discrete fractional derivative
• modified Mittag-Leffler function
• discrete Mittag-Leffler function
• discrete nabla Laplace transform
• convolution
• discrete ABR fractional derivative

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.

• 出版日期2016-9-5