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On the Definitions of Nabla Fractional Operators
Joint Authors
Merdivenci Atici, Ferhan
Abdeljawad (Maraaba), T.
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-11
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Abdeljawad (Maraaba), T.& Merdivenci Atici, Ferhan. 2012. On the Definitions of Nabla Fractional Operators. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-469612
Modern Language Association (MLA)
Abdeljawad (Maraaba), T.& Merdivenci Atici, Ferhan. On the Definitions of Nabla Fractional Operators. Abstract and Applied Analysis No. 2012 (2012), pp.1-13.
https://search.emarefa.net/detail/BIM-469612
American Medical Association (AMA)
Abdeljawad (Maraaba), T.& Merdivenci Atici, Ferhan. On the Definitions of Nabla Fractional Operators. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-469612
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-469612