Stability Solution of Fractional Randomly System

Eman Ahmad Hussen^1,*, Sameh ALargeh²

¹PhD Student, Homs University, College of Science, Homs, Syria

²Faculty Member, Homs University, Faculty of Science, Homs, Syria

Emails: e.hussain@homs-univ.edu.sy; salarje@homs-univ.edu.sy

Abstract

 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.

Keywords: Randomly Parameters; Norm, expected value; Lyapunov function; Integral inequalities; Stable; Mean sense; Laplace transform; Fractional derivative