Fractional Reaction-Diffusion Equations for Modelling Complex Biological Patterns
نویسندگان
چکیده
منابع مشابه
Numerical solutions for fractional reaction-diffusion equations
Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...
متن کامل2 00 6 Fractional Reaction - Diffusion Equations
In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of ge...
متن کاملOn the Speed of Spread for Fractional Reaction-Diffusion Equations
The fractional reaction diffusion equation ∂tu+Au = g(u) is discussed, where A is a fractional differential operator on R of order α ∈ (0, 2), the C function g vanishes at ζ = 0 and ζ = 1 and either g ≥ 0 on (0, 1) or g < 0 near ζ = 0. In the case of non-negative g, it is shown that solutions with initial support on the positive half axis spread into the left half axis with unbounded speed if g...
متن کاملFourier spectral methods for fractional-in-space reaction-diffusion equations
Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is computationally demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code al...
متن کاملStability of patterns in reaction-diffusion equations
These are lecture notes associated with the hour-long talk “Stability of patterns in reaction-diffusion equations,” given at the BU/Keio Workshop in Dynamical Systems, during Sept 15-19, 2014, at Boston University. The abstract of the talk was: “Reaction-diffusion equations model a wide variety of chemical and biological processes. Such systems are well known for exhibiting patterns, such as tr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Malaysian Journal of Fundamental and Applied Sciences
سال: 2014
ISSN: 2289-599X,2289-5981
DOI: 10.11113/mjfas.v8n3.135