The -Transform Method and Delta Type Fractional Difference Operators

Dorota Mozyrska and Małgorzata Wyrwas

Discrete Dynamics in Nature and Society, 2015, vol. 2015, 1-12

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:852734

DOI: 10.1155/2015/852734

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