The time fractional Klein–Kramers model (TFKKM) is obtained by incorporating the subdiffusive mechanisms into the Klein–Kramers formalism. The TFKKM can efficiently express subdiffusion while an external force field is present in the phase space. The model describes the escape of a particle over a barrier and has a significant role in examining a variety of systems including slow (subdiffusion) dynamics. This paper describes a hybrid algorithm adopting the local radial basis functions based finite difference (LRBF–FD) for the numerical solution of the TFKKM. The time discretization is accomplished via the Grünwald-Letnikov formulation with second-order accuracy and the spatial derivatives are discretized by the LRBF–FD. The LRBF–FD is based on the local support domain that causes to a more sparse matrix and overcomes the ill-conditioning associated with the global collocation. The convergence and stability analysis of the time-discrete algorithm are deduced using the energy method. The feasibility and applicability of the LRBF–FD are demonstrated by using irregular domains. Numerical results are compared with analytical solution and with those obtained by other techniques to verify the accuracy and validity of the LRBF–FD.

通过将次扩散机制纳入Klein-Kramers形式主义中，可以得到时间分数Klein-Kramers模型（TFKKM）。当在相空间中存在外力场时，TFKKM可以有效地表达扩散。该模型描述了粒子越过障碍物的逸出，并且在检查包括慢速（亚扩散）动力学在内的各种系统中具有重要作用。本文描述了一种混合算法，该算法采用基于局部径向基函数的有限差分（LRBF–FD）来求解TFKKM。时间离散化通过具有二次精度的Grünwald-Letnikov公式完成，而空间导数由LRBF–FD离散化。LRBF–FD基于局部支持域，该域导致矩阵更加稀疏，并克服了与全局搭配相关的不良条件。利用能量方法推导了时间离散算法的收敛性和稳定性。通过使用不规则域证明了LRBF-FD的可行性和适用性。将数值结果与解析解以及通过其他技术获得的数值进行比较，以验证LRBF–FD的准确性和有效性。