Numerical solution for a class of multi-order fractional differential equations with error correction and convergence analysis

Abstract

In this article, we investigate numerical solution of a class of multi-order fractional differential equations with error correction and convergence analysis. According to fractional differential definition in Caputo’s sense, fractional differential operator matrix is deduced. The problem is reduced to a set of algebraic equations, and we apply MATLAB to solve the equation. In order to improve the precision of numerical solution, the process of error correction for multi-order fractional differential equation is introduced. By constructing the multi-order fractional differential equation of the error function, the approximate error function is obtained so that the numerical solution is corrected. Then, we analyze the convergence of the shifted Chebyshev polynomials approximation function. Numerical experiments are given to demonstrate the applicability of the method and the validity of error correction.