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Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations

Author

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  • Jan Čermák
  • Tomáš Kisela
  • Luděk Nechvátal

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 ð ‘ž -difference calculus. Some of our results are new also in these particular discrete settings.

Suggested Citation

  • Jan Čermák & Tomáš Kisela & Luděk Nechvátal, 2011. "Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-21, June.
    • Handle: RePEc:hin:jnlaaa:565067
    DOI: 10.1155/2011/565067
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    Cited by:

    1. Du, Feifei & Jia, Baoguo, 2020. "Finite time stability of fractional delay difference systems: A discrete delayed Mittag-Leffler matrix function approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Wang, Mei & Du, Feifei & Chen, Churong & Jia, Baoguo, 2019. "Asymptotic stability of (q, h)-fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 158-167.
    3. I. Area & J. D. Djida & J. Losada & Juan J. Nieto, 2015. "On Fractional Orthonormal Polynomials of a Discrete Variable," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-7, July.

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