Feng Baolin, Feng Xue,ChuangYao, and Qiao Xing.  Numerical solution and dynamic properties of nonlinear fractional differential equation based on particle swarm optimization.  Dynamic Systems and Applications 29 (2020) No. 3, 579-593

https://doi.org/10.46719/dsa202029314

ABSRTACT.
Fractional differential equation is used more and more widely in various fields. At the same time, the development upsurge of fractional differential equation also drives its theory to improve day by day. This paper is devoted to the study and analysis of numerical solutions and dynamic properties of fractional differential equations. The method adopted is based on the advantages of particle swarm optimization algorithm (RP-PSO) with random disturbance, such as high success rate and more accurate optimization. Based on this method, a model is built, and the particle swarm optimization algorithm with random disturbance proposed in this paper is proved by simulation experiments (RP-PSO) can effectively solve some problems of numerical solution and dynamic properties of nonlinear fractional equation. The purpose of this paper is to provide new ideas for the study of fractional differential equations and their dynamic properties, so that more optimization algorithms can be applied to the field of numerical solution of fractional differential equations in the future, and make some contributions to this field.

Keywords. particle swarm optimization; algorithm; differential equation; dynamic properties