Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space

The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this research article is to present results on the numerical simulation for time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space that were found in the transonic flows. Those resulting mathematical models are solved using the reproducing kernel algorithm which provide appropriate solutions in term of infinite series formula. 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 prospects of the gained results and the algorithm are discussed through academic validations.