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 exact solutions. Liouville, Dodd-Bullough-Mikhailov (DBM), and Sinh-Gordon equations are the models under consideration. 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 equation method. The suggested method is applicable to several categories of nonlinear physical models and allows us to extract numerous generalized solutions in soliton and periodic forms The resulting solutions may also be directly compared with a number of findings obtained 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.