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The -Transform Method and Delta Type Fractional Difference Operators

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  • Dorota Mozyrska
  • Małgorzata Wyrwas

Abstract

The Caputo-, Riemann-Liouville-, and Grünwald-Letnikov-type difference initial value problems for linear fractional-order systems are discussed. We take under our consideration the possible solutions via the classical -transform method. We stress the formula for the image of the discrete Mittag-Leffler matrix function in the -transform. We also prove forms of images in the -transform of the expressed fractional difference summation and operators. Additionally, the stability problem of the considered systems is studied.

Suggested Citation

  • Dorota Mozyrska & Małgorzata Wyrwas, 2015. "The -Transform Method and Delta Type Fractional Difference Operators," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-12, March.
    • Handle: RePEc:hin:jnddns:852734
    DOI: 10.1155/2015/852734
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    Cited by:

    1. Pakhare, Sumit S. & Bhalekar, Sachin & Gade, Prashant M., 2022. "Synchronization in coupled integer and fractional-order maps," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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