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Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations
Joint Authors
Kisela, Tomáš
Nechvátal, Luděk
Čermák, Jan
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-28
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
This paper investigates some initial value problems in discrete fractional calculus.
We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the solution.
Then the structure of the solutions space is discussed, and, in a particular case, an explicit form of the general solution involving discrete analogues of Mittag-Leffler functions is presented.
All our observations are performed on a special time scale which unifies and generalizes ordinary difference calculus and q-difference calculus.
Some of our results are new also in these particular discrete settings.
American Psychological Association (APA)
Čermák, Jan& Kisela, Tomáš& Nechvátal, Luděk. 2011. Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-21.
https://search.emarefa.net/detail/BIM-481200
Modern Language Association (MLA)
Čermák, Jan…[et al.]. Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations. Abstract and Applied Analysis No. 2011 (2011), pp.1-21.
https://search.emarefa.net/detail/BIM-481200
American Medical Association (AMA)
Čermák, Jan& Kisela, Tomáš& Nechvátal, Luděk. Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-21.
https://search.emarefa.net/detail/BIM-481200
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-481200