This paper is concerned with a new fractional Jacobi collocation method for solving a system of multi-order fractional differential equations with variable coefficients. The existence, uniqueness, and smoothness results are rigorously studied. From the numerical point of view, first a new interpolation operator based on the orthogonal fractional Jacobi functions as well as its approximation properties are provided, and then it is employed to obtain collocation solution of the underlying problem. Moreover, the convergence analysis of the proposed scheme is investigated in both $L_{\infty }$ and $L^2$ norms. Finally, the applicability and validity of the method are demonstrated by means of some illustrative examples.

本文涉及一种新的分数雅可比搭配方法，用于求解变系数多阶分数阶微分方程组。对存在性，唯一性和平滑性结果进行了严格的研究。从数值的角度来看，首先提供了一种基于正交分数雅可比函数及其近似性质的新插值算子，然后将其用于获取基础问题的搭配解。此外，对两种方案的收敛性分析进行了研究。${\mathrm{大号}}_{\infty }$ 和 ${\mathrm{大号}}^2$规范。最后，通过一些实例说明了该方法的适用性和有效性。