aspg-34-3915-1792223311 20261017074831 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2024 4 2 Eman Ahmad Hussen PhD Student, Homs University, College of Science, Homs, Syria Sameh ALargeh Faculty Member, Homs University, Faculty of Science, Homs, Syria 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 15 21 3915 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.040203 https://americaspg.com/journal/34/article/3915 https://americaspg.com/storage/articles/manuscripts/01M1W17RS1E97S61X1G66JWCF1.pdf