Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications
Joint Authors
al-Mdallal, Q. M.
Abdeljawad (Maraaba), T.
Hajji, M. A.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-06-21
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Recently, Abdeljawad and Baleanu have formulated and studied the discrete versions of the fractional operators of order 0<α≤1 with exponential kernels initiated by Caputo-Fabrizio.
In this paper, we extend the order of such fractional difference operators to arbitrary positive order.
The extension is given to both left and right fractional differences and sums.
Then, existence and uniqueness theorems for the Caputo (CFC) and Riemann (CFR) type initial difference value problems by using Banach contraction theorem are proved.
Finally, a Lyapunov type inequality for the Riemann type fractional difference boundary value problems of order 2<α≤3 is proved and the ordinary difference Lyapunov inequality then follows as α tends to 2 from right.
Illustrative examples are discussed and an application about Sturm-Liouville eigenvalue problem in the sense of this new fractional difference calculus is given.
American Psychological Association (APA)
Abdeljawad (Maraaba), T.& al-Mdallal, Q. M.& Hajji, M. A.. 2017. Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1151378
Modern Language Association (MLA)
Abdeljawad (Maraaba), T.…[et al.]. Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-8.
https://search.emarefa.net/detail/BIM-1151378
American Medical Association (AMA)
Abdeljawad (Maraaba), T.& al-Mdallal, Q. M.& Hajji, M. A.. Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1151378
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151378