The -Transform Method and Delta Type Fractional Difference Operators

By Dorota Mozyrska, Malgorzata Wyrwas. 2015

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The Caputo-, Riemann-Liouville-, and Grunwald-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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/f687a601b6bcfb9f26e8db2b5e3808089074beb9