Abstract
In this manuscript, we work on the essential collocation technique via utilizing the shifted second Chebyshev polynomials type (SSCPT). The numeral technique for unraveling the nonlinear fractional Rubella ailment. The characteristic of the SSCPT is introduced. The dynamic system for this model is discussed. We proved the existence of a stable solution of the fractional model after and before control. The optimal control of this model and numerical technique for the simulation of the control problem is also discussed. The finite difference strategy has been utilized to fathom the arrangement of conditions. The numerical model is given to affirm the unwavering quality and adequacy of the suggested technique. The fad and importance of the results are clearing about the 3D plot. We are discussing free disease equilibrium, stability equilibrium point, and the existence of stable solution. It appears that the solutions acquired are novel and ability is helpful in analyzing the internal technique of other nonlinear biological models. Next applying the numerical technique, we are able to say that the outcomes we acquired are perfect, whether from an analytical or numerical point of view. Additionally, the numerical outcomes are completely consistent with the analytical outcomes. The numerical technique used in this manuscript to solve this model has not been utilized by any author before that. Also, this model with fractional derivatives defined in this way has not been studied before that. The techniques utilized are easy to effect, whether analytical or numerical and give good outcomes.