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Bachelor Thesis from the year 2021 in the subject Mathematics - Miscellaneous, Federal Urdu University, language: English, abstract: In this analysis, the explicit solutions to a generalized Korteweg-de Vries equation (KdV for short) with initial condition are calculated by using the new Analytical method.Korteweg-de Vries (KdV) equation, which are characterized by the solitary wave solutions of the classical nonlinear equations that lead to solitons. Here, the classical nonlinear equations of interest usually admit for the existence of a special type of the traveling wave solutions which are either solitary waves or solitons. Fractional Calculus (FC) goes back to the dawn of the theory of differential calculus. however, the application of FC just came up in the last two decades, due to the breakthrough in the area of chaos that disclose subtle connections with the FC concepts.