Nonlinear reaction with fractional dynamics

In this paper we consider a system of three fractional differential equations describing a nonlinear reaction. Our analysis includes both analytical technique and numerical simulation. This allows us to control the efficiency of the numerical method. We combine the numerical approximation of fractional integral with finding zeros of a function of one variable. The variable gives a desired solution. The solution has a peak. Its position in time depends on the order of fractional derivative. The two other solutions of this system have a completely monotonic character.