Open Access
2012 On the Definitions of Nabla Fractional Operators
Thabet Abdeljawad, Ferhan M. Atici
Abstr. Appl. Anal. 2012(SI01): 1-13 (2012). DOI: 10.1155/2012/406757


We show that two recent definitions of discrete nabla fractional sum operators are related. Obtaining such a relation between two operators allows one to prove basic properties of the one operator by using the known properties of the other. We illustrate this idea with proving power rule and commutative property of discrete fractional sum operators. We also introduce and prove summation by parts formulas for the right and left fractional sum and difference operators, where we employ the Riemann-Liouville definition of the fractional difference. We formalize initial value problems for nonlinear fractional difference equations as an application of our findings. An alternative definition for the nabla right fractional difference operator is also introduced.


Download Citation

Thabet Abdeljawad. Ferhan M. Atici. "On the Definitions of Nabla Fractional Operators." Abstr. Appl. Anal. 2012 (SI01) 1 - 13, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1253.39004
MathSciNet: MR2984037
Digital Object Identifier: 10.1155/2012/406757

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI01 • 2012
Back to Top