Computing bifurcations behavior of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types in Hilbert space with error analysis

Abstract

In this article, we propose and analyze a computational algorithm for the numerical solutions of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the -term of exact solutions, numerical solutions of linear and nonlinear singular time-fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such singular integrodifferential equations.