Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X Articles in Press 2026 06 30 A Hybrid Numerical Scheme for the Time-Fractional Telegraph Equation 2128 10.22128/ansne.2026.3271.1201 EN Seyyedeh Mitra Dabiri Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran Javad Damirchi Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran 0000-0002-4878-1921 Journal Article 2026 02 18 This study introduces a hybrid approach based on a finite difference scheme and radial basis functions (RBF) for solving the Caputo time--fractional telegraph equation numerically. To handle the temporal fractional derivatives, a finite difference formulation of the L1/L2 type is adopted, while the spatial derivatives are approximated using an RBF collocation technique. This combination results in a  discretized system characterized by a sparse matrix structure. Through the application of energy methods, the stability and convergence assessment of the temporal discretization is conducted, yielding a theoretical error estimate of $\mathcal{O}(\delta_t^{3-\alpha})$ in the time direction. The reliability and effectiveness of the proposed numerical scheme are verified through a representative test problem, confirming the capability of the proposed method to achieve high accuracy. Time–fractional telegraph equation Caputo derivative Collocation method Radial basis functions Stability and convergence https://ansne.du.ac.ir/article_2128_e45ed1632de9cb9748b153f7a70ec1b8.pdf