Mathematical modeling of time fractional reaction-diffusion systems
By V. Gafiychuk, B. Datsko, V. Meleshko. 2008
278 citations recorded by the source corpus.
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives. It is shown that by combining the fractional derivatives index with the ratio of characteristic times, it is possible to find the marginal value of the index where the oscillatory instability arises. The increase of the value of fractional derivative index leads to the time periodic solutions. The domains of existing periodic solutions for different parameters of the problem are obtained. A computer simulation of the corresponding nonlinear fractional ordinary differential equations is presented. For the fractional reaction-diffusion systems it is established that there exists a set of stable spatio-temporal structures of the one-dimensional system under the Neumann and periodic boundary conditions. The characteristic features of these solutions consist of the transformation of the steady-state dissipative structures to homogeneous oscillations or space temporary structures at a certain value of fractional index and the ratio of characteristic times of system.
Subfields: Computer Networks and Communications, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/b41626aa57b3acbe8ab1dfa3c7395709c489abce
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Networks and Communications
In Modeling and Simulation
In Public Health, Environmental and Occupational Health
Citations in the corpus
- Existence and Hyers‐Ulam stability of fractional nonlinear impulsive switched coupled evolution equations (2018, unknown): “Then the operator system provided by { p(t) = Υ1(p, q)(t), q(t) = Υ2(p, q)(t) (2) is called Hyers-Ulam stable if we can fined i(i = 1, 2, 3, 4) > 0, such that for each ρi(i = 1, 2) > 0 and for each solution (p∗, q∗) ∈ E of the inequalities given by { ||p∗ − Θ1(p, q∗)||PC ≤ ρ1, ||q∗ − Θ2(p, q∗)||PC ”
- Existence of solutions for fractional differential equations of order q∈(2,3] with anti-periodic boundary conditions (2010, background): “In view of the relations DIx(t) = x(t) and I Ix(t) = I q+px(t) for q,p > 0, x ∈ L(0,1) [9, 13, 16], we obtain x′(t) = ∫ t”