New traveling solutions of the fractional nonlinear KdV and ZKBBM equations with 𝒜ℬℛ fractional operator

Abstract

This research paper investigates novel explicit wave solutions of the fractional Korteweg–de Vries (KdV) equation and the fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation. These models are used as gravity models in water and an interaction model between the long waves. The Atangana–Baleanu ([Formula: see text]) fractional operator is utilized for the first time to convert the fractional form of both models into nonlinear partial differential equations with an integer order. The extended simplest equation method is employed to construct some distinct types of solitary wave solutions such as exponential, rational, hyperbolic and trigonometric functions. For more illustration of our obtained solutions, some figures for them are given. The power and practical properties of the used method are tested.