<p>This study focuses on formulating and examining a computational scheme aimed at solving a class of nonlinear time-fractional integro-differential equations characterized by weakly singular kernels. The mathematical model incorporates the Caputo derivative in the temporal domain together with integral operators in space to describe nonlocal effects. Initially, a semi-discrete formulation is derived through a linear spline approximation of the Caputo derivative. This is then extended to a complete discretization by applying finite difference techniques with non-uniform meshes along the spatial variables. The proposed scheme is analyzed in terms of stability and convergence through energy-based arguments. To validate the effectiveness of the approach, two test cases with known analytical solutions are investigated. Numerical results confirm both the accuracy and the predicted convergence behavior of the method. Overall, the framework introduced here offers a dependable and adaptable numerical strategy for handling fractional models arising in various scientific and engineering applications.</p>