Abdeljawad, ThabetBaleanu, Dumitru2017-04-242025-09-182017-04-242025-09-182016Abdeljawad, T., Baleanu, D. (2016). Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels. Advance in Difference Equations. http://dx.doi.org/10.1186/s13662-016-0949-51687-1847https://doi.org/10.1186/s13662-016-0949-5https://hdl.handle.net/20.500.12416/11571Abdeljawad, Thabet/0000-0002-8889-3768In 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.eninfo:eu-repo/semantics/openAccessDiscrete Fractional DerivativeModified Mittag-Leffler FunctionDiscrete Mittag-Leffler FunctionDiscrete Nabla Laplace TransformConvolutionDiscrete Abr Fractional DerivativeArticle10.1186/s13662-016-0949-52-s2.0-84986325930