相关论文: Mathematical modeling of pattern formation in sub-…

In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…

We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…

The object of this paper is to present a computable solution of a fractional partial differential equation associated with a Riemann-Liouville derivative of fractional order as the time-derivative and Riesz-Feller fractional derivative as…

In this study, the numerical solutions of reaction-diffusion systems are investigated via the trigonometric quintic B-spline nite element collocation method. These equations appear in various disciplines in order to describe certain…

Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response…

Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…

In this paper, we consider a time-fractional reaction-diffusion system with the same nonlinearities of the Newton-Leipnik chaotic system. Through analytical tools and numerical results, we derive sufficient conditions for the asymptotic…

Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…

Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…

In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…

High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…

Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…

We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the index properties, but they are not differentiable. We overcome the…

Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…

We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…

This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…

Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…

We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the refractive index properties, but they are not differentiable. We…

This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may…