In this paper, we have implemented an efficient and high accurate radial basis function (RBF) collocation scheme for solving nonlinear systems of q-fractional differential equations. We firstly convert the problems under investigation into the equivalent systems of weakly singular q-integral equations by some essential results of fractional q-calculus. Secondly, we combine RBF collocation method and Newton–Raphson iterative algorithm to solve the latter systems of weakly singular q-integral equations. More precisely, applying RBF collocation scheme will transform the system of q-integral equations into the associated system of nonlinear algebraic equations that can be solved by iterative methods such as the Newton–Raphson algorithm. Finally, various numerical test problems including linear and nonlinear examples are listed to illustrate the robustness of the proposed global scheme with respect to the at least two recent methods in the literature.

在本文中，我们实现了一种高效且高精度的径向基函数（RBF）配置方案，用于求解q分式微分方程的非线性系统。首先，我们通过分数q微积分的一些基本结果将研究中的问题转换为弱奇异q积分方程的等效系统。其次，我们将RBF配置方法与Newton-Raphson迭代算法结合起来，解决了后者的弱奇异q积分方程组。更精确地说，应用RBF搭配方案会将q积分方程组转换为非线性代数方程组的关联系统，可以通过诸如Newton–Raphson算法之类的迭代方法来求解。最后，