Study on numerical solution of a variable order fractional differential equation based on symmetric algorithm

Abstract

As the class of fractional differential equations with changing order has attracted more attention and attention in the fields of research and engineering, it is important to study its numerical solutions. Numerical solution algorithm for a class of fractional differential equations with transformed arrays based on the proposed symmetry algorithm. The symmetry classification is used for the class of values of the boundary problem of the fractional differential equation with the order of change. A fully symmetric classification of the boundary value problem for a class of fractional differential equations with variable sequences is determined by using a fully symmetric differential sequence sorting algorithm. The problem of the boundary value of the fractional differential equation with the transformed order is reduced to the initial value of the ordinary differential equation. The Legendre polynomial method is used to solve the numerical solution of the starting value of the differential equation. The common differential equation is transformed into a matrix series product by a different operator matrix. The matrix products are converted to algebraic equations by discrete variables. By solving the equations, the numerical solution of the starting value of the common differential equation is obtained.