The \(\mathcal{Z}\)-transform method and delta type fractional difference operators
type: Item
instance of: scholarly article
title: The \(\mathcal{Z}\)-transform method and delta type fractional difference operators
zbMATH Open document ID: 1418.44003
DOI: 10.1155/2015/852734
author: Dorota Mozyrska
author: Małgorzata Wyrwas
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 7025525
Wikidata QID: Q59105512
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/852734
OpenAlex ID: W2025282794
cites work: Q4351330
cites work: Q4233638
cites work: Comparison of h-Difference Fractional Operators
cites work: Multiparameter fractional difference linear control systems
cites work: Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems
cites work: Robust stability of positive discrete-time linear systems of fractional order
cites work: Fractional positive linear systems
cites work: Reachability of Cone Fractional Continuous-Time Linear Systems
cites work: Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
cites work: Stability of Discrete Fractional Order State-space Systems
cites work: Q3468036
cites work: Initial value problems in discrete fractional calculus
cites work: Q3087300
cites work: A semigroup-like property for discrete Mittag-Leffler functions
cites work: Necessary optimality conditions for fractional difference problems of the calculus of variations
cites work: Fractional \(h\)-difference equations arising from the calculus of variations
cites work: Discrete-time fractional variational problems
cites work: Discrete Mittag-Leffler functions in linear fractional difference equations
cites work: Exponential functions of discrete fractional calculus
cites work: Dynamic equations on time scales: A survey
cites work: The Laplace transform in discrete fractional calculus
cites work: On the asymptotic stability of linear system of fractional-order difference equations
cites work: Stability and asymptotic properties of a linear fractional difference equation
cites work: Stability regions for linear fractional differential systems and their discretizations
cites work: Overview of Fractional h-difference Operators
cites work: On Riemann and Caputo fractional differences
cites work: Controllability ofh-difference linear control systems with two fractional orders
cites work: Constrained Controllability of h-Difference Linear Systems with Two Fractional Orders
Recommended article: Q3824740
Recommended article: Q5708340
Recommended article: A generalized fractional difference operator and its applications
Recommended article: On the z-transform and the nonhomogeneous linear difference equations
Recommended article: Delayed linear difference equations: The method of Ƶ -transform
Recommended article: \(n\)-dimensional fractional frequency Laplace transform by the inverse difference operator
Recommended article: On Z-fractional differential equations
Recommended article: Zygmund-type estimates for fractional integration and differentiation operators of variable order
Recommended article: The zeros and poles of delta operator systems
description: scientific article; zbMATH DE number 7025525