Convergence Analysis Of Numerical Methods For Two Classes Of Fractional Differential Equations

Fractional differential equations are widely used in the fields of hydrology,signal processing,physics,biochemistry,control theory,etc.After in-depth exploration in recent decades,the relevant theories are very rich and there are a lot of research results.Because analytical solutions of many fractional differential equations are difficult to obtain,and even the analytical solutions for some nonlinear fractional differential equations cannot be obtained,which makes the study of numerical methods for fractional differential equations of great theoretical and practical significance.There have been many achievements in the research of numerical methods for fractional differential equations,but there is still a lot of work worthy of in-depth study.In this paper,for impulsive fractional differential equation and fractional delay differential equation,they are first converted into equivalent integral equations,the corresponding numerical schemes are obtained after the integral terms are discretized,and the numerical methods for solving these two types of problems are obtained.The convergence results of the numerical methods are obtained through the convergence analysis,the numerical results verify the correctness of the theoretical results obtained.