Exploring exact solutions for physical differential models through generalized derivatives

Abstract

In this study, we develop three well-known fractional differential physical models with novel,
precise solutions. Liouville, Dodd-Bullough-Mikhailov (DBM), and Sinh-Gordon equations are the models
in question. These models will be broken down into three nonlinear ordinary differential equations using
a waveform transformation, which can be precisely solved using the approach of the simplest equations.
The suggested method is applicable to several categories of nonlinear physical models and allows us to
extract numerous generalised solutions in soliton and periodic forms. The resulting answers may also
be directly compared with a number of findings made in the literature. Additionally, representations in
two- and three-dimensions are provided to show how changing the fractional parameter’s amount may
impact how monotonic the solutions are obtained.