Numerical Computation Of Fractional Dynamical System Model

As the main research object of system science and system theory,fractionalorder dynamic system is a generalization of integer-order dynamic system,which is mainly described and characterized by fractional-order differential equation.Since integer-order differential equations only depend on the local characteristics of functions,and fractional-order differential equations consider the whole information of functions in weighted form,so in many aspects,the application of fractional-order mathematical model can describe the dynamic response of real systems more accurately.Compared with integer-order differential equation,fractional-order differential equation is more complex,which means that the solution of fractional-order dynamic system model is more difficult.It is often difficult to obtain the timedependent or analytical solutions of the system,which need to be carried out by means of numerical computation.Therefore,it is particularly important to solve and simulate the fractional order dynamic system.Therefore,on the basis of in-depth study of the characteristics of various fractionalorder dynamic system models,this paper designs algorithms for solving fractionalorder differential equation systems,fractional-order impulsive differential equation systems and fractional-order delay differential equation systems respectively by combining qualitative analysis with quantitative analysis,and gives corresponding simulation examples.The simulation results show that these algorithms are feasible and have certain practicability and versatility.The purpose of this paper is not only to show the validity and generality of the numerical algorithm,but also to provide a reference method for numerical computation of general fractional-order dynamic system.