This work develops an efficient finite difference framework for a class of fractional Volterra-Fredholm integro-differential equations involving Caputo fractional derivatives of order \(\alpha \in (0,1)\) . The underlying problem typically exhibits a weak singularity at the initial time \(t = 0\) . To approximate the solution, a fully discrete scheme is constructed by coupling the classical \(L1\) discretization for the Caputo fractional derivative with a composite trapezoidal rule for both the Volterra and Fredholm integral operators on uniform mesh. A rigorous error analysis is carried out to establish the convergence behaviour of the proposed numerical scheme. It is shown that, due to the inherent weak singularity near the initial time, the global convergence rate depends explicitly on the fractional order \(\alpha\) , yielding \(\mathcal{O}((\Delta t)^{\alpha})\) , whereas first-order accuracy \(\mathcal{O}(\Delta t)\) is recovered on subdomains away from the origin. The theoretical findings are corroborated by numerical experiments, confirming the sharpness of the derived error bounds and demonstrating the reliability and efficiency of the proposed framework. The method thus provides a simple and robust approach for the numerical treatment of fractional integro-differential models arising in scientific and engineering applications.
