Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/3915 2022 2022 PhD Student, Homs University, College of Science, Homs, Syria Eman Eman Faculty Member, Homs University, Faculty of Science, Homs, Syria Sameh ALargeh In this paper, we study stability Solution of Fractional Randomly System. Two methods are provided to check the stability of such system in mean sense. The first method is based on integral inequalities. The second method is based on Lyapunov function. Stable in mean sense, asymptotically stable in mean sense are shown by using generalized Gromwell inequality. Stable in mean sense, asymptotically stable in mean sense, Mittag-Leffler stable in mean sense are shown by using generalized Lyapunov method. 2024 2024 23 36 10.54216/PAMDA.040203 https://www.americaspg.com/articleinfo/34/show/3915