In this chapter, we propose and analyze a computational algorithm for the numerical solutions of singular time-fractional partial differential equations of Dirichlet function types. By interrupting the n-term of exact solutions, numerical solutions of linear and non-linear singular time-fractional equations of non-homogeneous function type are studied from a mathematical viewpoint. The accuracy properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the presented algorithm and simulated annealing provide a good scheduling methodology to such singular fractional equations. © 2019 Walter de Gruyter GmbH, Berlin/Boston.