Solitons demonstrate an explanatory role in a multitude of physical phenomena in the scientific domain of the world. Owing to the non-availability of exact solutions in many non-linear physical problems, various analytical and non-analytical schemes have evolved. This study is concerned with the establishment of analytical solutions for nonlinear partial differential equations. With the evolution of time, the flourishing part of the fundamental phenomenon of soliton has gained considerable utility and the attention of researcher and scientists. Solitons are a special kind of nonlinear waves that are able to maintain their shape along with the promulgation. Few related problems have been discussed and resolved using Exp-Function Methods. The specific narrative aims to contribute an instinctive grasp for Exp-Function Method, Modified Exp-Function Exp method, Exp ))-Expansion Method and Novel Rational ))-Expansion Method. Moreover, these methods introduce several types of the solutions like hyperbolic, trigonometric and rational solutions. Likewise, we shall protract novel expansion method for the problems occurring in mathematical physics of varied differential equations. The proposed methods are capable of determining nonlinear differential equations, their systems and several differential equations of fractional order. The Multiple Exp-function Method has been employed as N-soliton solution to different problems, which further elaborates the efficacy and accuracy of the proposed algorithm.