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2011 Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations
Jan Čermák, Tomáš Kisela, Luděk Nechvátal
Abstr. Appl. Anal. 2011(SI1): 1-21 (2011). DOI: 10.1155/2011/565067


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.


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Jan Čermák. Tomáš Kisela. Luděk Nechvátal. "Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations." Abstr. Appl. Anal. 2011 (SI1) 1 - 21, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1220.39010
MathSciNet: MR2817254
Digital Object Identifier: 10.1155/2011/565067

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI1 • 2011
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