scholarly journals IMPACT OF THE SAME DEGENERATE ADDITIVE NOISE ON A COUPLED SYSTEM OF FRACTIONAL SPACE DIFFUSION EQUATIONS

Fractals ◽  
2021 ◽  
Author(s):  
WAEL W. MOHAMMED ◽  
NAVEED IQBAL
Keyword(s):  
Stochastic System ◽  
Additive Noise ◽  
Coupled System ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Volterra System ◽  
Fractional Diffusion Equations ◽  
Brusselator Model ◽  
The Stability ◽  
Fractional Space

In this paper, we present a class of stochastic system of fractional space diffusion equations forced by additive noise. Our goal here is to approximate the solutions of this system via a system of ordinary differential equations. Moreover, we study the influence of the same degenerate additive noise on the stability of the solutions of the stochastic system of fractional diffusion equations. We are interested in the systems that have nonlinear polynomial and give applications as Lotka–Volterra system from biology and the Brusselator model for the Belousov–Zhabotinsky chemical reaction from chemistry to illustrate our results.

scholarly journals Approximate Solutions of the Space-Fractional Diffusion Equations with Additive Noise

2021 ◽  
Author(s):  
Wael W. Mohammed ◽  
Hijaz Ahmad
Keyword(s):  
Additive Noise ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Critical Dynamics ◽  
Ginzburg Landau ◽  
Fractional Diffusion Equations ◽  
Stochastic Space ◽  
Polynomial Term ◽  
Fractional Space

Abstract In this article we take into account a class of stochastic space diffusion equations with polynomials forced by additive noise. We derive rigorously limiting equations which de…ne the critical dynamics. Also, we approximate solutions of stochastic fractional space di¤usion equations with polynomial term by limiting equations, which are ordinary di¤er-ential equations. Moreover, we address the e¤ect of the noise on the solution’s stabilization. Finally, we apply our results to Fisher’s equation and Ginzburg–Landau models.

Continuous time random walk models associated with distributed order diffusion equations

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Sabir Umarov
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Diffusion Processes ◽  
Stability Index ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Analytic Method ◽  
Fractional Diffusion Equations ◽  
The Stability ◽  
Distributed Order

AbstractIn this paper continuous time and discrete random walk models approximating diffusion processes associated with time-fractional and spacedistributed order differential equations are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change process is the inverse to a Levy’s stable subordinator with the stability index β ∈ (0, 1). In the paper the convergence of modeled continuous time and discrete random walks to time-changed processes associated with distributed order fractional diffusion equations are proved using an analytic method.

Finite difference scheme for the time-space fractional diffusion equations

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Jianxiong Cao ◽  
Changpin Li
Keyword(s):  
Finite Difference ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Stability And Convergence ◽  
Finite Difference Schemes ◽  
Order Accuracy ◽  
Fractional Diffusion Equations ◽  
Time Space ◽  
Liouville Fractional Derivative ◽  
The Stability

AbstractIn this paper, we derive two novel finite difference schemes for two types of time-space fractional diffusion equations by adopting weighted and shifted Grünwald operator, which is used to approximate the Riemann-Liouville fractional derivative to the second order accuracy. The stability and convergence of the schemes are analyzed via mathematical induction. Moreover, the illustrative numerical examples are carried out to verify the accuracy and effectiveness of the schemes.

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