Legendre多项式求解变系数的分数阶Fredholm积分微分方程

为了求解变系数分数阶Fredholm微积分方程的数值解,运用Caputo分数阶导数及性质,得出了由Legendre多项式构造的任意分数阶微分算子Dα,再利用区间［0,1］上Legendre级数的逼近,将变系数的分数阶微积分方程用矩阵形式表示,采用配点法,得到相应的代数方程组,对原微积分方程的数值解进行了研究并给出了数值算例,验证了Legendre多项式方法的可行性和有效性。

Legendre polynomial method for solving Fredholm integro-differential equations of fractional order with variable coefficient

In order to solve the Fredholm integro-differential equations of fractional order with variable coefficient, By using Caputo fractional derivative and property, the arbitrary order derivatives expressed by Legendre polynomial are acquired, then using Legendre series on the approximation in the interval, the fractional integral differential equations can be changed into matrix form of the equation, using collocation method. The original integral differential equations numerical solution are obtained. A numerical example is presented, which verifying the feasibility and effectiveness of the method.