Evaluation of the performance of fractional evolution equations based on fractional operators and sensitivity assessment

In this article, the nonlinear fractional Kudryashov’s equation and the space–time fractional nonlinear Tzitzeica–Dodd–Bullough (TDB) equation are solved using the new auxiliary equation method, which yields innovative analytical solutions using β and M-Truncated fractional derivatives. The fractional wave and Painlevé transformations are implemented to transform the space and time fractional nonlinear equations into a nonlinear ordinary differential equation. The model solutions are compared by utilizing the two fractional derivatives. Hyperbolic, trigonometric, rational, exponential, and other sorts of soliton solutions are discovered, and these forms of the outcomes illustrate the superiority of the method’s uniqueness. The solutions provided in this piece are sophisticated and comprehensive, and the results of the literature review are one instance of the findings. The key advantage of this approach over remedies is that it possesses higher options with flexible constraints. By plotting 3D as well as 2D graphs of the acquired results and analyzing the effect of the fractional parameter ρ on the wave profiles of the phenomenon, it has been determined that the fractional parameter significantly affects the wave profiles. The findings are carried out in such a way as to showcase the applicability and expertise of fractional derivatives and the proposed approach to evaluate several nonlinear fractional partial differential equations. Finally, the comprehensive sensitivity analysis of the proposed models is done by first transforming it into the format of a planer dynamical system using the Galilean transformation.