New analytical and numerical solutions to the (2+1)-dimensional conformable cpKP–BKP equation arising in fluid dynamics, plasma physics, and nonlinear optics

This study investigates the \((2+1)\)-dimensional conformable combined potential Kadomtsev–Petviashvili-B-type Kadomtsev–Petviashvili (cpKP–BKP) equation. It is a linear combination of potential KP and BKP systems. This equation sheds light on hydrodynamics, plasma physics, and nonlinear optics. Firstly, conformable derivative definitions and their characteristics are provided. Next, using the modified extended tanh-function approach, accurate analytical solutions to this problem are obtained. The residual power series method (RPSM) was then used to investigate the approximate solutions to the model. A table compares the obtained findings with absolute errors. The 3D and 2D surfaces and the corresponding contour plot surfaces of specifically gathered data illustrate the obtained findings’ physical aspect. The physical activity of the problem can only be tracked with explicit solutions that have been accomplished. The results illustrate how the under-investigation and other nonlinear physical models from mathematical physics are applied in real life. All of the solutions obtained are new and do not exist in the literature. Consequently, these methods might produce notable outcomes in obtaining the exact and approximate solutions of fractional differential equations (FDEs) in various circumstances.