Existence of Solutions and Relative Controllability of a Stochastic System with Nonpermutable Matrix Coefficients

被引：6

作者：

Abuasbeh, Kinda ^{[1
]}

Mahmudov, Nazim I. ^{[2
]}

Awadalla, Muath ^{[1
]}

机构：

[1] King Faisal Univ, Coll Sci, Dept Math & Stat, Hafuf 31982, Al Ahsa, Saudi Arabia

[2] Eastern Mediterranean Univ, Dept Math, TR-99628 Famagusta, Turkey

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 06期

关键词：

stochastic equation; existence; uniqueness; relative controllability; approximate controllability; APPROXIMATE CONTROLLABILITY; EVOLUTION-EQUATIONS; DIFFERENTIAL-EQUATIONS; FRACTIONAL ORDER; LINEAR-SYSTEMS; MILD SOLUTIONS; DELAY; STABILITY;

D O I：

10.3390/fractalfract6060307

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this study, time-delayed stochastic dynamical systems of linear and nonlinear equations are discussed. The existence and uniqueness of the stochastic semilinear time-delay system in finite dimensional space is investigated. Introducing the delay Gramian matrix, we establish some sufficient and necessary conditions for the relative approximate controllability of time-delayed linear stochastic dynamical systems. In addition, by applying the Banach fixed point theorem, we establish some sufficient relative approximate controllability conditions for semilinear time-delayed stochastic differential systems. Finally, concrete examples are given to illustrate the main results.

引用

页数：18

共 53 条

[1] Existence and uniqueness results for a class of fractional stochastic neutral differential equations [J].

Ahmadova, Arzu ;

Mahmudov, Nazim, I .

CHAOS SOLITONS & FRACTALS, 2020, 139

[2]

Aimene D., 2020, Nonlinear Dyn. Syst. Theory, V20, P465

[3] A variation of constant formula for Caputo fractional stochastic differential equations [J].

Anh, P. T. ;

Doan, T. S. ;

Huong, P. T. .

STATISTICS & PROBABILITY LETTERS, 2019, 145 :351-358

[4]

[Anonymous], 1993, DELAY DIFFERENTIAL E, DOI DOI 10.1016/S0076-5392(08)X6164-8

[5] APPROXIMATE CONTROLLABILITY OF SEMILINEAR FRACTIONAL STOCHASTIC SYSTEM WITH NONLOCAL CONDITIONS [J].

Arora, Urvashi ;

Sukavanam, N. .

DYNAMIC SYSTEMS AND APPLICATIONS, 2018, 27 (01) :45-62

[6] On concepts of controllability for deterministic and stochastic systems [J].

Bashirov, AE ;

Mahmudov, NI .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (06) :1808-1821

[7] Existence and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators [J].

Bedi, Pallavi ;

Kumar, Anoop ;

Abdeljawad, Thabet ;

Khan, Zareen A. ;

Khan, Aziz .

ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

[8] Approximate Controllability of a Class of Semilinear Hilfer Fractional Differential Equations [J].

Bora, Swaroop Nandan ;

Roy, Bandita .

RESULTS IN MATHEMATICS, 2021, 76 (04)

[9] Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses [J].

Dhayal, Rajesh ;

Malik, Muslim .

CHAOS SOLITONS & FRACTALS, 2021, 151

[10] Representation of solutions of discrete delayed system x(k+1)=Ax(k)+Bx(k-m)+f(k) with commutative matrices [J].

Diblík, J ;

Khusainov, DY .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 318 (01) :63-76

← 1 2 3 4 5 6 →