On the solutions of some nonlinear fractional partial differential equations using an innovative and direct procedure

In this article, a highly effective technique is implemented to obtain the approximate solutions of strongly nonlinear fractional order partial differential equations (NFPDEs). The findings of this study show the successful behavior of the fractional novel analytical method (FNAM), which can be used successfully for the solutions of common, severe NFPDEs. In the proposed method, the nonlinearity in each mathematical model is directly handled by using fractional Taylor series, which reduces the calculation effort. In this work, the method's strength is primarily demonstrated on NFPDEs, and the obtained results are displayed via graphs and tables. From the numerical simulations, it is evident that the suggested technique has greater accuracy despite smaller calculations. It is the most straightforward method for determining the formulaic solution to any type of NFPDE and is considered to be the unique numerical methodology.