Abstract
The analysis of nonlinear events related to physical phenomena is a popular issue in the modern day. The essential purpose of this work is to discover a novel approximate solution to the fractional nonlinear Benjamin Bona Mahony Peregrine Burgers equation (BBMPB) utilizing the natural decomposition method (NDM) of fractional order. The suggested approach provides analytical solutions that are extremely near to the exact solution obviating the complexities associated with many other approaches. The expected issue’s uniqueness theorem and convergence analysis are explored using Banach’s fixed-point theory. The reliability and accuracy of the recommended method were tested using numerical simulations. The graphs and tables reflect the results. The comparison of the suggested scheme’s solution with the exact solutions demonstrates that the scheme is efficient, methodical, and extremely exact in tackling nonlinear complicated phenomena.