The objectives of this research describes a novel meshless technique for solving space–time fractional Burgers’ equation by using concept of weighted and Caputo fractional derivative type. An efficient and accurate meshfree method based on backward substitution method and finite difference method is applied for problem on the various computational domain with scattering nodes. According to proposal method, Crank–Nicolson techniques is exploited to find the approximation in time level and the backward substitution method is utilized to compute node on the boundary. Subsequently, we obtain the corresponding weighted parameters the governing equations, we implemented collocation approach based on radial basis function. To eliminate nonlinearity, quasilinearization technique is applied to transform nonlinear source term into a linear source term. For investigation accuracy and reliably, this paper is compared with other previous researches. It is found that proposed scheme outperforms compared with existing numerical method.

本研究的目标是通过使用加权和Caputo分数阶导数类型的概念，描述一种新颖的无网格技术，用于求解时空分数Burgers方程。针对具有散射节点的各种计算域上的问题，采用了一种基于向后替换法和有限差分法的高效，精确的无网格方法。根据提议的方法，利用Crank–Nicolson技术找到时间水平的近似值，并使用向后替换方法计算边界上的节点。随后，我们获得了相应的加权参数控制方程，并基于径向基函数实现了配置方法。为了消除非线性，应用了拟线性化技术将非线性源项转换为线性源项。为了提高调查的准确性和可靠性，将本文与其他先前的研究进行了比较。结果表明，与已有的数值方法相比，该方案具有更好的性能。