Convergence Analysis of Implicit Euler Method for a Class of Nonlinear Impulsive Fractional Differential Equations

Abstract

For a class of nonlinear impulsive fractional differential equations, we first transform them into equivalent integral equations, and then the implicit Euler method is adapted for solving the problem. The convergence analysis of the method shows that the method is convergent of the first order. The numerical results verify the correctness of the theoretical results.