Nonlinear reaction with fractional dynamics

TL;DR

This paper investigates a nonlinear reaction system modeled by fractional differential equations, combining analytical and numerical methods to analyze solution behavior, including peak positioning and monotonicity.

Contribution

It introduces a novel numerical approach for fractional differential systems and analyzes solution characteristics, especially the peak position influenced by fractional order.

Findings

Solution peak position depends on fractional derivative order

Numerical method effectively approximates fractional integrals

Two solutions exhibit complete monotonicity

Abstract

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.