 This paper studies the effects of the third-order dispersion parameter on the traveling wave solutions of the fractional extended non-linear Schrodinger equation. It uses the extended simple equation approach and the improved F expansion method to secure a variety of distinct solutions in the form of dark, singular, periodic, rational, and exponential waves. Additionally, the stability of the outcomes is evaluated. Graphs have been drawn to support the reported findings. The authors also show that the third-order dispersion parameter can significantly affect the stability of the solutions. The main purpose of this study is to obtain the different types of traveling wave solutions of the fractional extended NLSE, which are absent in the literature. These novel solutions hold a prominent place in the fields of non-linear sciences and optical engineering as they enable a thorough understanding of the development and dynamic nature of such models. This article was authored by Jamshead Ahmed, Sonja Akram, Kansa Noor, and others.