Redouane Douaifia

Saad Dahlab University · Faculty of Technology

In this paper, we propose a numerical scheme of the predictor–corrector type for solving nonlinear fractional initial value problems; the chosen fractional derivative is called the Atangana–Baleanu derivative defined in Caputo sense (ABC). This proposed method is based on Lagrangian quadratic polynomials to approximate the nonlinearity implied in t...

The aim of this paper is to study the existence and the asymptotic stability of solutions for an epidemiologically emerging reaction-diffusion model. We show that the model has two types of equilibrium points to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between indi...

The aim of this paper is to study the dynamics of a reaction‐diffusion SI (susceptible‐infectious) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We prove that the proposed model has two steady states under one condition. By analyzing the eigenvalues and using the linearizat...

This thesis seeks primarily to contribute to an attempt to understand the patterns we see in nature, such as pigmentation in animals, branching in trees and skeletal structures, as well as how the vast range of patterns and structures emerge from an almost uniformly homogeneous fertilized egg, through survey and study as well as improve a number of...

In this paper, we propose a numerical scheme of the predictor-corrector type for solving nonlinear fractional initial value problems, the chosen fractional derivative is called the Atangana-Baleanu derivative defined in Caputo sense (ABC). This proposed method is based on Lagrangian quadratic polynomials to approximate the nonlinearity implied in t...

This work mainly focuses on the dynamics of an epidemiologically emerging reaction-diffusion system. We establish global presence and the outcomes of asymptotic local and global stability to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals by means of t...

This paper primarily seeks to extend the results of Rebiai and Benachour [10] on the global existence, uniqueness, uniform boundedness, and the asymptotic behavior of solutions for a weakly coupled reaction-diffusion systems with exponential nonlinearity on a growing domain with an isotropic growth, the desired results are obtained by using Lyapuno...

This paper deals with a coupled two-cell Schnakenberg reaction-diffusion system subject to Neumann boundary conditions. Firstly, we obtain the global existence and uniqueness of classical solution for the system and under certain conditions for the parameters, we obtain the asymptotic stability. Then, with the aim of displaying the dynamics of sugg...

This paper presents a new predictor–corrector numerical scheme suitable for fractional differential equations. An improved explicit Atangana–Seda formula is obtained by considering the neglected terms and used as the predictor stage of the proposed method. Numerical formulas are presented that approximate the classical first derivative as well as t...

The main purpose of this paper is to extend the result of Barabanova (Proc. Am. Math. Soc. 122:827–831, 1994) on the global existence, uniqueness, uniform boundedness, and the asymptotic behavior of solutions for a weakly coupled class of reaction-diffusion systems on a growing domain with an isotropic growth. Numerical simulations are used to affi...

A coupled two-cell Brusselator system subject to Neumann boundary conditions is considered. Firstly, we obtain the global existence of classical solutions for the system. Then, with the aim of showing the model dynamics, we develop a positivity preserving splitting technique to find the numerical solution of the proposed model. The numerical scheme...

Reaction-diffusion equations containing fractional derivatives can provide adequate mathematical models for explaining anomalous diffusion and transport dynamics in complex systems that can not be adequately modeled by standard numerical order equations. Researchers have recently found that many physical processes display fractional order dynamics...

The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We prove that the proposed model has two steady states under one condition. By analyzing the eigenvalues and using...

This paper presents a new predictor-corrector numerical scheme suitable for fractional differential equations. An improved explicit Atangana-Seda formula is obtained by considering the neglected terms and used as the predictor stage of the proposed method. Numerical formulas are presented that approximate the classical first derivative as well as t...

Recently, fractional derivative has been widely used in the modeling of complex physical and mechanical phenomena in wide classes of complex media with hereditary, fractal and non-markovian properties, is a field of rapidly growing interest with applications in many different fields. Reaction–diffusion systems of partial differential equations are...

In this work, we present numerical method for solving one-dimensional variable order time fractional reaction diffusion system with delay. The numerical method are obtained considering the Method of Lines (MOL) approach, MOL is a general way of viewing a partial differential equation as a system of ordinary differential equations. The partial deriv...

This paper establishes conditions for the asymptotic stability of time--fractional reaction--diffusion systems. The stability of linear systems is investigated by means of the eigenfunction expansion of the Laplacian operator. Theoretical bounds are placed on the arguments of the infinity of eigenvalues belonging to the instant Jacobian matrix. Non...

The purpose of this work is to present numerical solutions of variable-order fractional delay differential equations with multiple lags based on the Adams-Bashforth-Moulton method, where the derivative is defined in the Caputo variable-order fractional sense. Since the variable-order fractional derivatives contain classical and fractional derivativ...