Abstract and Applied Analysis

Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations

Jan Čermák, Tomáš Kisela, and Luděk Nechvátal

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2011, Number 1 (2011), Article ID 565067, 21 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171419

Digital Object Identifier
doi:10.1155/2011/565067

Mathematical Reviews number (MathSciNet)
MR2817254

Zentralblatt MATH identifier
1220.39010

Citation

Čermák, Jan; Kisela, Tomáš; Nechvátal, Luděk. Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations. Abstr. Appl. Anal. 2011 (2011), no. 1, Article ID 565067, 21 pages. doi:10.1155/2011/565067. https://projecteuclid.org/euclid.aaa/1313171419


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