In this article, the fractional order time-varying linear dynamical system defined by Caputo derivative is investigated. Laplace transform collocation method (LTCM) and Daftar-Gejii-Jafaris method (DGJM) are used to find the approximation solution of this equation. Using the Laplace transform collocation method, a new form of trial function from the original equation is presented. The unknown coefficients in the trial functions are calculated by using collocation method. LTCM gives a good result for the numerical solution of this equation. Providing DGJM converges, it is shown that obtained approximate solution is effective which is close to the exact solution. Then, the exact solution is compared with these approximate solutions. The results showed that the methods are effective and useful. These methods produced better approximations than the ones produced with the standard weighted residual methods.

本文研究了由Caputo导数定义的分数阶时变线性动力系统。拉普拉斯变换搭配法（LTCM）和Daftar-Gejii-Jafaris方法（DGJM）用于寻找该方程的近似解。使用拉普拉斯变换搭配方法，从原始方程中提出了一种新形式的试验函数。试验函数中的未知系数采用搭配法计算。LTCM 给出了该方程的数值解的良好结果。当DGJM收敛时，表明得到的近似解是有效的，接近于精确解。然后，将精确解与这些近似解进行比较。结果表明这些方法是有效和有用的。