This paper aims to establish a robust numerical method utilizing a finite difference scheme combined with a meshless approach to investigate the two-dimensional stochastic time-fractional telegraph equation on non-rectangular domains. Initially, a forward finite difference technique is applied to manage the time variable, followed by implementing a meshless method that employs radial basis functions (RBFs) for spatial function approximation. This approach simplifies the problem, converting the two-dimensional stochastic time-fractional telegraph equation into a linear system of algebraic equations, which can be efficiently solved. A significant benefit of this method lies in the inherent flexibility of meshless techniques. Additionally, the meshless framework can be easily adapted to tackle various high-dimensional problems across both regular and irregular domains. To evaluate the effectiveness and precision of the proposed method, several test problems are presented. The numerical results obtained demonstrate the method’s capability to solve the two-dimensional stochastic time-fractional telegraph equation.
