Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels Article Swipe

View

Related Concepts

invertible matrix mathematics fractional calculus mittag-leffler function ordinary differential equation discrete time and continuous time function (biology) applied mathematics partial differential equation pure mathematics algebra over a field mathematical analysis differential equation biology statistics evolutionary biology

Thabet Abdeljawad , Dumitru Băleanu ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1186/s13662-016-0949-5 · OA: W2516345384

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.