Controllability of fractional stochastic delay dynamical systems

2020/09/22 by Arzu Ahmadova, Ahmadova, Arzu, Ismail T. Huseynov +3
Mathematics · Economics, Econometrics and Finance · #Nonlinear Differential Equations Analysis #Stochastic processes and financial applications #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.2009.10654

Abstract

In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic analogue of variation of constants formula via a newly defined delayed Mittag-Leffer type matrix function. Thus, we investigate new results on existence and uniqueness of mild solutions with the help of weighted maximum norm to fractional stochastic time-delay differential equations whose coefficients satisfy standard Lipschitz conditions. The main points in the proof are to apply Ito's isometry and martingale representation theorem, and to show the notion of a coincidence between the integral equation and the mild solution. Finally, we study complete controllability results for linear and nonlinear fractional stochastic delay dynamical systems with Wiener noise.

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