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The fundamental intention of this article is to find several soliton solutions to the generalized Benjamin–Bona–Mahony equation. The fractional derivatives are described in the conformable sense. These solutions are generated using the functional variable approach. Then, we acquire via this technique some distinctive solutions, such as the singular soliton, periodic soliton, bell-shaped soliton, and kink soliton solutions. The fundamental feature of the demonstrated method is that it's convenient and provides precise, effective solutions to nonlinear equations. The solutions given will offer a thorough examination of this model and any associated occurrences. [ABSTRACT FROM AUTHOR]

The current manuscript proposes an innovative approach for obtaining exact solutions to the conformable time-fractional nonlinear differential-difference equations (NDDEs). The fundamental concept of this approach involves the generalized exponential rational function method (GERFM). In this method, the exact solutions include trigonometric and hyperbolic functions. In order to assess this method's efficacy, we consider its application to the conformable time-fractional Hybrid Lattice equation. After solving this model, we provide its dynamic behavior through the 3D, 2D, and Contour graphs. The soliton solutions obtained are used to describe any related physical phenomena. [ABSTRACT FROM AUTHOR]

In this article, we focus on a specific version of the NDDEs which is the relativistic Toda lattice equation. We employ the generalized exponential rational function method on a nonlinear model of surface wave propagation to recognize their diverse singular soliton and multi-soliton wave structures. What is remarkable in this article is the use of graphic diagrams, which have diversified the solutions for solving such equations, leading to a greater understanding of the movements of particles and the strengthening of nonlinear lattice dynamics. The efficiency and strength of the employed method are illustrated, signifying its applicability to a wide spectrum of NDDEs in physical phenomena. [ABSTRACT FROM AUTHOR]

The principal purpose of this research is to utilize the exp-function approach for achieving exact solutions of nonlinear optical fibers, including fractional order in the sense of conformable derivatives. Owing to the algorithm of symbolic computational, Some soliton solutions are obtained, including solitary soliton, singular kink-type soliton, and periodic solitons. These results are generated and developed by using the exp-function. To the greatest of our knowledge, the soliton solutions given in this study could be highly beneficial in comprehending physical phenomena. [ABSTRACT FROM AUTHOR]

In this paper, the generalized rational function procedure was used to produce new solitary solutions to the fractional Jaulent–Miodek hierarchy equation. The equation is shortly called the Jaulent–Miodek equation, which was first derived by Jaulent and Miodek and associated with energy-dependent Schrödinger potentials. The equation is converted into a fourth-order partial differential equation using a transformation. In order, we find some solitary solutions such as soliton, rational and hyperbolic function solutions of Jaulent–Miodek hierarchy equation by the help of generalized exponential rational function procedure. Then, for some parameters, we draw three-dimensional graphics of real values of some exact solutions that we acquired by using this procedure. [ABSTRACT FROM AUTHOR]