TY - GEN
T1 - The Fractional-Order Selkov-Schnakenberg Reaction-Diffusion Model
T2 - International Conference on Fractional Calculus and Applications, ICFCA 2024
AU - Jebril, Iqbal H.
AU - Bendib, Issam
AU - Ouannas, Adel
AU - Boulaaras, Salah
AU - Batiha, Iqbal M.
AU - Momani, Shaher
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025
Y1 - 2025
N2 - This paper investigates the Fractional-Order Selkov-Schnakenberg Reaction-Diffusion (FOSSRD) model, a mathematical framework for studying spatiotemporal dynamics, including pattern formation and stability, in chemical and biological systems. The model integrates fractional calculus to capture memory and hereditary effects inherent in complex systems. A comprehensive analysis is conducted, covering local asymptotic stability (LAS) of equilibrium points (EPs) and the impact of key parameters, such as diffusion coefficients and fractional orders (FOs), on dynamic behavior. Semi-analytical solutions and numerical simulations validate the theoretical findings, illustrating the system’s ability to generate diverse spatial patterns and oscillatory dynamics. Applications of the model span biochemical oscillations, cellular signaling pathways, and ecological interactions. The results provide deeper insights into the intricate mechanisms governing nonlinear systems and establish a foundation for further research in higher-dimensional and stochastic extensions of the model.
AB - This paper investigates the Fractional-Order Selkov-Schnakenberg Reaction-Diffusion (FOSSRD) model, a mathematical framework for studying spatiotemporal dynamics, including pattern formation and stability, in chemical and biological systems. The model integrates fractional calculus to capture memory and hereditary effects inherent in complex systems. A comprehensive analysis is conducted, covering local asymptotic stability (LAS) of equilibrium points (EPs) and the impact of key parameters, such as diffusion coefficients and fractional orders (FOs), on dynamic behavior. Semi-analytical solutions and numerical simulations validate the theoretical findings, illustrating the system’s ability to generate diverse spatial patterns and oscillatory dynamics. Applications of the model span biochemical oscillations, cellular signaling pathways, and ecological interactions. The results provide deeper insights into the intricate mechanisms governing nonlinear systems and establish a foundation for further research in higher-dimensional and stochastic extensions of the model.
KW - Fractional-order
KW - Local asymptotic stability
KW - Selkov-Schnakenberg model
UR - https://www.scopus.com/pages/publications/105021002076
U2 - 10.1007/978-3-031-95381-1_1
DO - 10.1007/978-3-031-95381-1_1
M3 - Conference contribution
AN - SCOPUS:105021002076
SN - 9783031953804
T3 - Springer Proceedings in Mathematics and Statistics
SP - 1
EP - 22
BT - Fractional Calculus and Applications, ICFCA 2024
A2 - Naifar, Omar
A2 - Ben Makhlouf, Abdellatif
A2 - Ben Makhlouf, Abdellatif
A2 - Hammami, Mohamed Ali
PB - Springer
Y2 - 26 December 2024 through 30 December 2024
ER -