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On Delta and Nabla Caputo Fractional Differences and Dual Identities
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-14
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We investigate two types of dual identities for Caputo fractional differences.
The first type relates nabla and delta type fractional sums and differences.
The second type represented by the Q-operator relates left and right fractional sums and differences.
Two types of Caputo fractional differences are introduced; one of them (dual one) is defined so that it obeys the investigated dual identities.
The relation between Riemann and Caputo fractional differences is investigated, and the delta and nabla discrete Mittag-Leffler functions are confirmed by solving Caputo type linear fractional difference equations.
A nabla integration by parts formula is obtained for Caputo fractional differences as well.
American Psychological Association (APA)
Abdeljawad (Maraaba), T.. 2013. On Delta and Nabla Caputo Fractional Differences and Dual Identities. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-469633
Modern Language Association (MLA)
Abdeljawad (Maraaba), T.. On Delta and Nabla Caputo Fractional Differences and Dual Identities. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-469633
American Medical Association (AMA)
Abdeljawad (Maraaba), T.. On Delta and Nabla Caputo Fractional Differences and Dual Identities. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-469633
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-469633