The improved singular boundary method (ISBM) and dual reciprocity method (DRM) are coupled to solve fractional derivative the Rayleigh–Stokes problem with nonhomogeneous term. This method is free of mesh and integration, mathematically simple, and easy to program. Also, origin intensity factors (OIFs) significant techniques in ISBM make the method as a strong meshless method. First, the time-fractional derivative term in mentioned equation is discretized; then, ISBM–DRM is utilized to solve consequent equation. It is proved the method is unconditionally stable and convergent with convergence order \({\mathcal {O}}(\tau ^{1+\alpha })\). In addition, numerical results confirm the accuracy and efficiency of the presented scheme.

改进的奇异边界法 (ISBM) 和对偶互易法 (DRM) 相结合，以解决具有非齐次项的瑞利-斯托克斯问题的分数阶导数。这种方法没有网格和积分，数学上简单，易于编程。此外，ISBM 中的原始强度因子 (OIF) 重要技术使该方法成为一种强大的无网格方法。首先，对上述方程中的时间分数阶导数项进行离散化；然后，ISBM-DRM 用于求解后续方程。证明了该方法无条件稳定且收敛，收敛阶数为\({\mathcal {O}}(\tau ^{1+\alpha })\)。此外，数值结果证实了所提出方案的准确性和效率。