Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics: A Study Using the Selkov-Schnakenberg Model

Issam Bendib; Adel Ouannas; Shaher Momani; Chaouki Aouiti

doi:10.1007/978-3-031-95381-1_2

Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics: A Study Using the Selkov-Schnakenberg Model

Issam Bendib
, Adel Ouannas
, Shaher Momani
, Chaouki Aouiti

Nonlinear Dynamic Research Centre (NDRC)

Frères Mentouri Constantine 1 University
University of Oum El Bouaghi
University of Jordan
University of Carthage

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

Abstract

This paper investigates the finite-time stability (FTS) of reaction-diffusion systems (RDs) governed by fractional-order (FO) dynamics, with a specific focus on the Selkov-Schnakenberg (SS) model. The study introduces theoretical stability conditions using Lyapunov function (LF)-based methods and Caputo fractional derivatives (CFD), providing a robust framework for analyzing equilibrium properties and synchronization in these systems. Numerical simulations validate the theoretical findings, demonstrating the system’s dynamic behavior under specified spatial and temporal conditions. The results highlight the influence of diffusion coefficients and reaction parameters on achieving FTS and underscore the practical applicability of the framework in modeling biological and chemical processes. This research contributes to the growing field of fractional-order systems, offering insights into their stability and synchronization within finite time frames.

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	23-39
Number of pages	17
ISBN (Print)	9783031953804
DOIs	https://doi.org/10.1007/978-3-031-95381-1_2
State	Published - 2025
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

Finite-time stability
Fractional-order
Lyapunov methods
Selkov-Schnakenberg model

Access to Document

10.1007/978-3-031-95381-1_2

Cite this

Bendib, I., Ouannas, A., Momani, S., & Aouiti, C. (2025). Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics: A Study Using the Selkov-Schnakenberg Model. In O. Naifar, A. Ben Makhlouf, A. Ben Makhlouf, & M. A. Hammami (Eds.), Fractional Calculus and Applications, ICFCA 2024 (pp. 23-39). (Springer Proceedings in Mathematics and Statistics; Vol. 505). Springer. https://doi.org/10.1007/978-3-031-95381-1_2

Bendib, Issam ; Ouannas, Adel ; Momani, Shaher et al. / Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics : A Study Using the Selkov-Schnakenberg Model. Fractional Calculus and Applications, ICFCA 2024. editor / Omar Naifar ; Abdellatif Ben Makhlouf ; Abdellatif Ben Makhlouf ; Mohamed Ali Hammami. Springer, 2025. pp. 23-39 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{b43644dd76eb4b45a9cc8d5e56fe1f5d,

title = "Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics: A Study Using the Selkov-Schnakenberg Model",

abstract = "This paper investigates the finite-time stability (FTS) of reaction-diffusion systems (RDs) governed by fractional-order (FO) dynamics, with a specific focus on the Selkov-Schnakenberg (SS) model. The study introduces theoretical stability conditions using Lyapunov function (LF)-based methods and Caputo fractional derivatives (CFD), providing a robust framework for analyzing equilibrium properties and synchronization in these systems. Numerical simulations validate the theoretical findings, demonstrating the system{\textquoteright}s dynamic behavior under specified spatial and temporal conditions. The results highlight the influence of diffusion coefficients and reaction parameters on achieving FTS and underscore the practical applicability of the framework in modeling biological and chemical processes. This research contributes to the growing field of fractional-order systems, offering insights into their stability and synchronization within finite time frames.",

keywords = "Finite-time stability, Fractional-order, Lyapunov methods, Selkov-Schnakenberg model",

author = "Issam Bendib and Adel Ouannas and Shaher Momani and Chaouki Aouiti",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; International Conference on Fractional Calculus and Applications, ICFCA 2024 ; Conference date: 26-12-2024 Through 30-12-2024",

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language = "English",

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Bendib, I, Ouannas, A, Momani, S & Aouiti, C 2025, Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics: A Study Using the Selkov-Schnakenberg Model. 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. 23-39, International Conference on Fractional Calculus and Applications, ICFCA 2024, Sousse, Tunisia, 26/12/24. https://doi.org/10.1007/978-3-031-95381-1_2

Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics: A Study Using the Selkov-Schnakenberg Model. / Bendib, Issam; 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. 23-39 (Springer Proceedings in Mathematics and Statistics; Vol. 505).

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

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T1 - Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics

T2 - International Conference on Fractional Calculus and Applications, ICFCA 2024

AU - Bendib, Issam

AU - Ouannas, Adel

AU - Momani, Shaher

AU - Aouiti, Chaouki

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

PY - 2025

Y1 - 2025

N2 - This paper investigates the finite-time stability (FTS) of reaction-diffusion systems (RDs) governed by fractional-order (FO) dynamics, with a specific focus on the Selkov-Schnakenberg (SS) model. The study introduces theoretical stability conditions using Lyapunov function (LF)-based methods and Caputo fractional derivatives (CFD), providing a robust framework for analyzing equilibrium properties and synchronization in these systems. Numerical simulations validate the theoretical findings, demonstrating the system’s dynamic behavior under specified spatial and temporal conditions. The results highlight the influence of diffusion coefficients and reaction parameters on achieving FTS and underscore the practical applicability of the framework in modeling biological and chemical processes. This research contributes to the growing field of fractional-order systems, offering insights into their stability and synchronization within finite time frames.

AB - This paper investigates the finite-time stability (FTS) of reaction-diffusion systems (RDs) governed by fractional-order (FO) dynamics, with a specific focus on the Selkov-Schnakenberg (SS) model. The study introduces theoretical stability conditions using Lyapunov function (LF)-based methods and Caputo fractional derivatives (CFD), providing a robust framework for analyzing equilibrium properties and synchronization in these systems. Numerical simulations validate the theoretical findings, demonstrating the system’s dynamic behavior under specified spatial and temporal conditions. The results highlight the influence of diffusion coefficients and reaction parameters on achieving FTS and underscore the practical applicability of the framework in modeling biological and chemical processes. This research contributes to the growing field of fractional-order systems, offering insights into their stability and synchronization within finite time frames.

KW - Finite-time stability

KW - Fractional-order

KW - Lyapunov methods

KW - Selkov-Schnakenberg model

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DO - 10.1007/978-3-031-95381-1_2

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AN - SCOPUS:105021007419

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T3 - Springer Proceedings in Mathematics and Statistics

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A2 - Hammami, Mohamed Ali

PB - Springer

Y2 - 26 December 2024 through 30 December 2024

ER -

Bendib I, Ouannas A, Momani S, Aouiti C. Finite-Time Stability Analysis of Reaction-Diffusion Systems with Fractional-Order Dynamics: A Study Using the Selkov-Schnakenberg Model. In Naifar O, Ben Makhlouf A, Ben Makhlouf A, Hammami MA, editors, Fractional Calculus and Applications, ICFCA 2024. Springer. 2025. p. 23-39. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-031-95381-1_2