Stability Investigation of Nonlinear Fractional Difference Equations with Incommensurate Orders

Noureddine Djenina; Adel Ouannas; Shaher Momani; Giuseppe Grassi

doi:10.1007/978-3-031-95381-1_10

Stability Investigation of Nonlinear Fractional Difference Equations with Incommensurate Orders

Noureddine Djenina
, Adel Ouannas
, Shaher Momani
, Giuseppe Grassi

University of Oum El Bouaghi
University of Jordan
University of Salento

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This study focuses on developing novel criteria for assessing the stability of nonlinear incommensurate fractional-order difference systems (FoDS), modeled using the Caputo difference operator. The proposed criteria are supported by rigorous proofs utilizing the Lyapunov function method. The theoretical findings are verified through numerical simulations, demonstrating stability in the considered systems.

Original language	English
Title of host publication	Fractional Calculus and Applications, ICFCA 2024
Editors	Omar Naifar, Abdellatif Ben Makhlouf, Abdellatif Ben Makhlouf, Mohamed Ali Hammami
Publisher	Springer
Pages	171-182
Number of pages	12
ISBN (Print)	9783031953804
DOIs	https://doi.org/10.1007/978-3-031-95381-1_10
State	Published - 2025
Externally published	Yes
Event	International Conference on Fractional Calculus and Applications, ICFCA 2024 - Sousse, Tunisia Duration: 26 Dec 2024 → 30 Dec 2024

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	505
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Fractional Calculus and Applications, ICFCA 2024
Country/Territory	Tunisia
City	Sousse
Period	26/12/24 → 30/12/24

Keywords

Caputo difference operator
Caputo differential operator
Incommensurate order continuous system
Incommensurate order discrete system
Lyapunov function

Access to Document

10.1007/978-3-031-95381-1_10

Cite this

Djenina, N., Ouannas, A., Momani, S., & Grassi, G. (2025). Stability Investigation of Nonlinear Fractional Difference Equations with Incommensurate Orders. In O. Naifar, A. Ben Makhlouf, A. Ben Makhlouf, & M. A. Hammami (Eds.), Fractional Calculus and Applications, ICFCA 2024 (pp. 171-182). (Springer Proceedings in Mathematics and Statistics; Vol. 505). Springer. https://doi.org/10.1007/978-3-031-95381-1_10

Djenina, Noureddine ; Ouannas, Adel ; Momani, Shaher et al. / Stability Investigation of Nonlinear Fractional Difference Equations with Incommensurate Orders. Fractional Calculus and Applications, ICFCA 2024. editor / Omar Naifar ; Abdellatif Ben Makhlouf ; Abdellatif Ben Makhlouf ; Mohamed Ali Hammami. Springer, 2025. pp. 171-182 (Springer Proceedings in Mathematics and Statistics).

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abstract = "This study focuses on developing novel criteria for assessing the stability of nonlinear incommensurate fractional-order difference systems (FoDS), modeled using the Caputo difference operator. The proposed criteria are supported by rigorous proofs utilizing the Lyapunov function method. The theoretical findings are verified through numerical simulations, demonstrating stability in the considered systems.",

keywords = "Caputo difference operator, Caputo differential operator, Incommensurate order continuous system, Incommensurate order discrete system, Lyapunov function",

author = "Noureddine Djenina and Adel Ouannas and Shaher Momani and Giuseppe Grassi",

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Djenina, N, Ouannas, A, Momani, S & Grassi, G 2025, Stability Investigation of Nonlinear Fractional Difference Equations with Incommensurate Orders. in O Naifar, A Ben Makhlouf, A Ben Makhlouf & MA Hammami (eds), Fractional Calculus and Applications, ICFCA 2024. Springer Proceedings in Mathematics and Statistics, vol. 505, Springer, pp. 171-182, International Conference on Fractional Calculus and Applications, ICFCA 2024, Sousse, Tunisia, 26/12/24. https://doi.org/10.1007/978-3-031-95381-1_10

Stability Investigation of Nonlinear Fractional Difference Equations with Incommensurate Orders. / Djenina, Noureddine; Ouannas, Adel; Momani, Shaher et al.
Fractional Calculus and Applications, ICFCA 2024. ed. / Omar Naifar; Abdellatif Ben Makhlouf; Abdellatif Ben Makhlouf; Mohamed Ali Hammami. Springer, 2025. p. 171-182 (Springer Proceedings in Mathematics and Statistics; Vol. 505).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Djenina N, Ouannas A, Momani S, Grassi G. Stability Investigation of Nonlinear Fractional Difference Equations with Incommensurate Orders. In Naifar O, Ben Makhlouf A, Ben Makhlouf A, Hammami MA, editors, Fractional Calculus and Applications, ICFCA 2024. Springer. 2025. p. 171-182. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-031-95381-1_10