The fractional differential equation has been used to describe many phenomenons in almost all applied sciences, such as fluid flow in porous materials, anomalous diffusion transport, acoustic wave propagation in viscoelastic materials, and others. In some cases, it is complicated to find the analytical solution of a fractional differential equation, so there are some special techniques to approximate the solution. In this paper, a new collocation method for a class of semilinear fractional differential equations has been constructed. The convergence properties of the proposed methods and the computational complexity are treated. Some numerical experiments are presented to validate the theoretical results. The proposed numerical method provides an alternative way to study some physical phenomena by fractional differential equations.

分数阶微分方程已被用于描述几乎所有应用科学中的许多现象，例如多孔材料中的流体流动、异常扩散传输、粘弹性材料中的声波传播等。在某些情况下，找到分数阶微分方程的解析解很复杂，因此有一些特殊的技术来逼近该解。本文构造了一类半线性分数阶微分方程的新搭配方法。处理了所提出方法的收敛性和计算复杂度。提出了一些数值实验来验证理论结果。所提出的数值方法提供了一种通过分数阶微分方程研究某些物理现象的替代方法。