In this article, we propose and analyze a computational method for the numerical solutions of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types. The method provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n-term of exact solutions, numerical solutions of linear and nonlinear singular time-fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. The utilized results show that the present method and simulated annealing provide a good scheduling methodology to such singular integrodifferential equations