Nowadays, fractional calculus has been a topic of interest in several areas of applied science and engineering because of the nonlocal character of its fractional operators, which provides additional information that allows a deep analysis of the mathematical models involved. Within fractional calculus, the qualitative approach to generalized ordinary differential equations or fractional order is an open subject of study, in which stability analysis plays a fundamental role in various applied models. This paper aims to present the foundational and recent results of the qualitative study of fractional order linear ordinary differential equations focused on the stability and some analytical methods used. This article presents and describes the fundamental results of the stability of systems of linear fractional order ordinary primary tools that can apply to various models of applied sciences and engineering. Keywords: fractional analysis, linear fractional differential equations, qualitative analysis, stability of fractional differential equations, linearization method. https://doi.org/10.55463/issn.1674-2974.50.10.5