一类非线性分数阶比例延迟微分方程的样条配置解法

摘要

提出求解一类非线性分数阶比例延迟微分方程的样条配置法,将其等价转化为弱奇性积分方程,利用Lagrange插值函数的基本思想,求出弱奇性积分方程的近似解,给出该方法的收敛性证明和误差估计.与Ghasemi等的结果(2015年)比较,数值算例说明本方法更有效.本方法不仅对线性、弱非线性分数阶比例延迟微分方程有效,对一些强非线性分数阶比例延迟微分方程依旧有效.%A spline collocation method is proposed for solving a class of nonlinear fractional differential equation with proportional delay.This kind of equation was first changed equivalently into the weakly singular integral equation.Then the approximate solution of the weakly singular integral equation is obtained by using the basic thought of Lagrange interpolation.The convergence proof and error estimation of the proposed method are obtained.Through comparing with the result of Ghasemi,et al (2015),the final numerical examples confirm the validity of our method.The proposed method is quite effective for solving linear,weakly nonlinear and some strongly nonlinear fractional differential equations with proportional delay.