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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]

This article aims to study the generalized exponential rational function method to solve the differential-difference Burgers' equation. Our approach is an efficient method for solving nonlinear partial differential equations, and it can be used for a specific type of nonlinear differential-difference equations. To recognize diverse singular soliton and multi-soliton wave structures, we displayed the 3-D and contour graphs associated with the solutions. [ABSTRACT FROM AUTHOR]

The paper discusses investigating the behavior of the discrete nonlinear Schrödinger (DNLS) system. This technique combines the exponential function method and the rational function method to obtain exact solutions for a wide range of nonlinear differential-difference equations (NDDEs). The objective is to utilize the generalized exponential rational function (GERF) technique to analyze and understand the dynamics of the DNLS system. Overall, this research contributes to advancing our knowledge of nonlinear dynamics in optical fibers and establishes a solid foundation for further exploration of soliton applications. • We focused on investigating discrete soliton solutions in a system that describes the propagation. • The investigation of these soliton solutions opens up new avenues for applications in optical communications. • We discovered various families of soliton solutions. [ABSTRACT FROM AUTHOR]

The ultimate focus of this research is to provide soliton solutions to the nonlinear differential-difference equations via conformable fractional derivatives which arise from the polarization of the ferroelectric nanoparticles. The investigation of achieved soliton solutions will provide effective results of ferroelectric materials and their related phenomena. [ABSTRACT FROM AUTHOR]