Solving the fractional nonlinear dispersive K(m, n, 1) partial differential equation: techniques and applications

Abstract This paper presents an in-depth analysis of fractional nonlinear dispersive K(m,n,1) equations using two innovative mathematical techniques: These two are the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM). These methods are used to formulate approximate analytical solutions in the framework of the Caputo operator. The MTIM offers an iterative type solution for fractional differential equations, and the MRPSM gives a series-based solution where nonlinearities are addressed efficiently. The effectiveness of these methods are illustrated through tables and figures, which can impress with their demonstrable result. They also demonstrate that our approaches of MTIM and MRPSM are adequate for solving the fractional nonlinear dispersive equations, which are enhanced compared with the conventional methods. This work significantly enriches the system's knowledge of applying sophisticated mathematical tools to interdisciplinary fractional differential equation problems with diverse bearings in numerous scientific and engineering disciplines.