  We consider an inverse source two-parameter sub-diffusion model subject to a
nonlocal initial condition. The problem models several physical processes,
among them are the microwave heating and light propagation in photoelectric
cells. A bi-orthogonal pair of bases is employed to construct a series
representation of the solution and a Volterra integral equation for the source
term. We develop a numerical algorithm for approximating the unknown
time-dependent source term. Due to the singularity of the solution near $t=0$,
a graded mesh is used to improve the convergence rate. Numerical experiments
are provided to illustrate the expected analytical order of convergence.
