Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (2)

Search Parameters:
Keywords = discrete-time fractional reaction-diffusion Lengyel–Epstein system

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
14 pages, 431 KiB  
Article
Synchronization of Fractional Partial Difference Equations via Linear Methods
by Ibraheem Abu Falahah, Amel Hioual, Mowafaq Omar Al-Qadri, Yazan Alaya AL-Khassawneh, Abdallah Al-Husban, Tareq Hamadneh and Adel Ouannas
Axioms 2023, 12(8), 728; https://doi.org/10.3390/axioms12080728 - 27 Jul 2023
Cited by 14 | Viewed by 1404
Abstract
Discrete fractional models with reaction-diffusion have gained significance in the scientific field in recent years, not only due to the need for numerical simulation but also due to the stated biological processes. In this paper, we investigate the problem of synchronization-control in a [...] Read more.
Discrete fractional models with reaction-diffusion have gained significance in the scientific field in recent years, not only due to the need for numerical simulation but also due to the stated biological processes. In this paper, we investigate the problem of synchronization-control in a fractional discrete nonlinear bacterial culture reaction-diffusion model using the Caputo h-difference operator and a second-order central difference scheme and an L1 finite difference scheme after deriving the discrete fractional version of the well-known Degn–Harrison system and Lengyel–Epstein system. Using appropriate techniques and the direct Lyapunov method, the conditions for full synchronization are determined.Furthermore, this research shows that the L1 finite difference scheme and the second-order central difference scheme may successfully retain the properties of the related continuous system. The conclusions are proven throughout the paper using two major biological models, and numerical simulations are carried out to demonstrate the practical use of the recommended technique. Full article
(This article belongs to the Special Issue Advances in Difference Equations)
Show Figures

Figure 1

16 pages, 416 KiB  
Article
On Fractional-Order Discrete-Time Reaction Diffusion Systems
by Othman Abdullah Almatroud, Amel Hioual, Adel Ouannas and Giuseppe Grassi
Mathematics 2023, 11(11), 2447; https://doi.org/10.3390/math11112447 - 25 May 2023
Cited by 14 | Viewed by 2550
Abstract
Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in [...] Read more.
Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in a diversity of disciplines. Thus, in this paper, we investigate the discrete-time fractional-order Lengyel–Epstein system as a model of the chlorite iodide malonic acid (CIMA) chemical reaction. With the help of the second order difference operator, we describe the fractional discrete model. Furthermore, using the linearization approach, we established acceptable requirements for the local asymptotic stability of the system’s unique equilibrium. Moreover, we employ a Lyapunov functional to show that when the iodide feeding rate is moderate, the constant equilibrium solution is globally asymptotically stable. Finally, numerical models are presented to validate the theoretical conclusions and demonstrate the impact of discretization and fractional-order on system dynamics. The continuous version of the fractional-order Lengyel–Epstein reaction–diffusion system is compared to the discrete-time system under consideration. Full article
Show Figures

Figure 1

Back to TopTop