The \(\mathcal{Z}\)-transform method and delta type fractional difference operators
Summary: 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 \(\mathcal{Z}\)-transform method. We stress the formula for the image of the discrete Mittag-Leffler matrix function in the \(\mathcal{Z}\)-transform. We also prove forms of images in the \(\mathcal{Z}\)-transform of the expressed fractional difference summation and operators. Additionally, the stability problem of the considered systems is studied.
scientific article; zbMATH DE number 7025525
scientific article