<p>This paper presents a hybrid method for obtaining approximate solutions to the distributed-order time-fractional telegraph equation. The proposed hybrid method integrates linear B-spline functions and local radial basis functions to create a robust and efficient numerical framework for tackling this class of equations. The process begins with the approximation of the Caputo fractional derivative in time using linear B-spline functions, which provides an accurate and straightforward representation of the temporal fractional dynamics. Subsequently, the distributed-order integral, a crucial component for modeling memory and hereditary effects, is estimated through a quadrature rule that ensures both precision and computational efficiency. In the second step, the local radial basis functions approach is used to approximate the spatial component of the equation. This technique offers flexibility and accuracy in handling spatial variations, making it suitable for problems involving complex geometries or irregular boundaries. A comprehensive stability and error analysis is conducted to ensure the reliability and convergence of the proposed method. These analyses demonstrate that the approach is well-suited for solving distributed-order fractional equations with high accuracy. Finally, several numerical examples are presented to illustrate the method’s efficiency and applicability. The results highlight the capability of the hybrid approach in addressing challenges in distributed-order fractional differential equations, paving the way for its application in broader scientific and engineering problems.</p>