New perspective to the fractal Konopelchenko–Dubrovsky equations with M-truncated fractional derivative

Abstract

In this work, for the first ever, the fractal Konopelchenko–Dubrovsky equations is defined by using a new fractional derivative called [Formula: see text]-truncated fractional derivative. The main goal of this work is to seek new type of fractal solitary wave solutions for the fractal Konopelchenko–Dubrovsky equations by a novel mathematical scheme, which is called variational sech-function method. The forms of these new fractal solitary wave solutions are different from those in the existing literature. Ultimately, the fractal dynamic behavior of these derived fractal solitary wave solutions is illustrated via a number of 3D and 2D simulation graphs with different parameters and fractal dimensions. The proposed new method can be employed to other nonlinear wave equations in mathematical physics with the same fractional derivative.