Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems

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...

Almost sure exponential stability of stochastic reaction diffusion systems with Markovian jump

The stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use Markovian jumps to model stochastic reaction diffusion systems‎. ‎In this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps‎. ‎Under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

Stochastic Simulation of Reaction-Diffusion Systems

Stochastic Simulation of Reaction-Diffusion Systems

Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear par...

Spatial-Stochastic Simulation of Reaction-Diffusion Systems

In biological systems, biochemical networks play a crucial role, implementing a broad range of vital functions from regulation and communication to resource transport and shape alteration. While biochemical networks naturally occur at low copy numbers and in a spatial setting, this fact often is ignored and well-stirred conditions are assumed for simplicity. Yet, it is now increasingly becoming...