On the Stability of Incommensurate h-Nabla Fractional-Order Difference Systems

Noureddine Djenina; Adel Ouannas; Taki Eddine Oussaeif; Giuseppe Grassi; Iqbal M. Batiha; Shaher Momani; Ramzi B. Albadarneh

doi:10.3390/fractalfract6030158

On the Stability of Incommensurate h-Nabla Fractional-Order Difference Systems

Noureddine Djenina
, Adel Ouannas
, Taki Eddine Oussaeif
, Giuseppe Grassi
, Iqbal M. Batiha
, Shaher Momani
, Ramzi B. Albadarneh

Nonlinear Dynamic Research Centre (NDRC)

University of Oum El Bouaghi
Ajman University
University of Salento
Irbid National University
University of Jordan
Hashemite University

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with the help of using some theoretical schemes, such as the Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem and Banach fixed point theorem. These results are verified numerically via two illustrative numerical examples that show the stabilities of the solutions of systems at hand.

Original language	English
Article number	158
Journal	Fractal and Fractional
Volume	6
Issue number	3
DOIs	https://doi.org/10.3390/fractalfract6030158
State	Published - Mar 2022

Keywords

Z-transform method
incommensurate fractional-order difference systems
stability analysis
the h-nabla fractional-order sum operator

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10.3390/fractalfract6030158

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title = "On the Stability of Incommensurate h-Nabla Fractional-Order Difference Systems",

abstract = "This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with the help of using some theoretical schemes, such as the Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem and Banach fixed point theorem. These results are verified numerically via two illustrative numerical examples that show the stabilities of the solutions of systems at hand.",

keywords = "Z-transform method, incommensurate fractional-order difference systems, stability analysis, the h-nabla fractional-order sum operator",

author = "Noureddine Djenina and Adel Ouannas and Oussaeif, \{Taki Eddine\} and Giuseppe Grassi and Batiha, \{Iqbal M.\} and Shaher Momani and Albadarneh, \{Ramzi B.\}",

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AU - Djenina, Noureddine

AU - Ouannas, Adel

AU - Oussaeif, Taki Eddine

AU - Grassi, Giuseppe

AU - Batiha, Iqbal M.

AU - Momani, Shaher

AU - Albadarneh, Ramzi B.

PY - 2022/3

Y1 - 2022/3

N2 - This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with the help of using some theoretical schemes, such as the Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem and Banach fixed point theorem. These results are verified numerically via two illustrative numerical examples that show the stabilities of the solutions of systems at hand.

AB - This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with the help of using some theoretical schemes, such as the Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem and Banach fixed point theorem. These results are verified numerically via two illustrative numerical examples that show the stabilities of the solutions of systems at hand.

KW - Z-transform method

KW - incommensurate fractional-order difference systems

KW - stability analysis

KW - the h-nabla fractional-order sum operator

UR - https://www.scopus.com/pages/publications/85127040173

U2 - 10.3390/fractalfract6030158

DO - 10.3390/fractalfract6030158

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JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 3

M1 - 158

ER -

On the Stability of Incommensurate h-Nabla Fractional-Order Difference Systems

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Keywords

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