Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion

Complex‐domain stability criteria for fractional‐order linear dynamical systems

“…The suggested criteria apply to various FCO-LTI systems, both single and multiple in fractional-order calculus, scalar and multivariable in input-output dimension, including the regularorder systems as the special cases. To extend the idea to other complicated fractional-order systems, say time-delayed [18], stochastic [19,20] and hybrid ones [21] are among our subsequent topics. Also interestingly, the factors β( ⋅ , ⋅ ) and α( ⋅ , ⋅ ) may be utilised for stabilisation [4,[22][23][24] or disturbance rejection [2] as design freedoms.…”

Stability analysis of fractional-order systems with randomly time-varying parameters

“…In order to find out the essential performance of the established equations, the existence and stability of the solutions of the equations is the first prerequisite. In the last few years, several results on this topic were presented including asymptotic stability [1,4,15,24]), exponential stability [2,25] and Mittag-Leffler stability [5,19,[27][28][29][30]. The general method for analyzing the stability is based on the first method of Lyapunov, the second method of Lyapunov and other mathematical techniques.…”

Boundary controllability of nonlocal Hilfer fractional stochastic differential systems with fractional Brownian motion and Poisson jumps

“…(see [2][3][4]). Stochastic differential equations driven by fractional Brownian motion have been considered extensively by research community in various aspects due to the salient features for real world problems (see [5][6][7][8][9][10][11][12]). In addition, controllability problems for different kinds of dynamical systems have been studied by several authors (see [13][14][15][16][17][18][19][20][21]), and the references therein.…”