scholarly journals Fractional Diffusion on Bounded Domains

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
Ozlem Defterli ◽  
Marta D’Elia ◽  
Qiang Du ◽  
Max Gunzburger ◽  
Rich Lehoucq ◽  
...  
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Diffusion Theory ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Nonlocal Diffusion ◽  
Bounded Domains ◽  
Fractional Diffusion Equations ◽  
Fractional Differential ◽  
Well Posed

AbstractThe mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. This paper discusses the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

An identification problem involving fractional differential variational inequalities

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tran Dinh Ke ◽  
Tran Van Tuan
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Identification Problem ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
Fractional Differential ◽  
Differential Variational Inequalities ◽  
Fixed Point Techniques

AbstractWe study the solvability and stability for the problem of identifying parameter in a class of fractional differential variational inequalities. Our approach is based on a regularity analysis for fractional diffusion equations and fixed point techniques.

scholarly journals Global Stability for Fractional Diffusion Equations in Biological Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Global Stability ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Lyapunov Functionals ◽  
Biological Models ◽  
Fractional Partial Differential Equations ◽  
Fractional Diffusion Equations ◽  
Fractional Differential

This paper proposes a new method of construction of Lyapunov functionals for the dynamical systems described by fractional differential equations and fractional partial differential equations. The proposed method is rigorously presented. Furthermore, the method is applied to establish the global stability of some fractional biological models with and without diffusion.

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