配置法解基于分数阶C^(α)空间的比例延迟微分方程

A New Collocation Method for Solving Fractional Pantograph Differential Equations Based on the Fractional C^(α)Space

不同于以往的文章,基于分数阶空间提出了一种新的算法,用于求解分数阶比例延迟微分方程并建立了一套完整的理论体系。通过数值实验结果,表明了本文所提出的算法通过少量计算就能获得较高精度的数值解,且易于操作。

In this paper,a new collocation method based on fractional spline is proposed for solving fractional pantograph differential equations.For solving the equation,the difficulties lie in choosing the space of the exact solution.In this paper,we solve the issue perfectly by proposing the concept of the fractional space.Meanwhile,a base of this fractional space is obtained.Based on the fractional space,a strict theory for obtaining the approximate solution is established.Finally,some examples are discussed for demonstrating the validity and applicability of our method and a small amount of calculation can gain an accurate number which satisfies the application requirements.