Exact Null Controllability of Sobolev-Type Hilfer Fractional Stochastic Differential Equations with Fractional Brownian Motion and Poisson Jumps

被引：41

作者：

Ahmed, Hamdy M. ^{[1
]}

Wang, JinRong ^{[2
,3
]}

机构：

[1] El Shorouk Acad, Higher Inst Engn, Dept Phys & Engn Math, Cairo, Egypt

[2] Guizhou Univ, Dept Math, Guiyang 55002, Guizhou, Peoples R China

[3] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2018年 / 44卷 / 03期

关键词：

Sobolev type stochastic differential equations; Fractional Brownian motion; Poisson jumps; Hilfer fractional derivative; Exact null controllability; SEMILINEAR INTEGRODIFFERENTIAL-SYSTEMS; APPROXIMATE CONTROLLABILITY; POSITIVE SOLUTIONS; EVOLUTION SYSTEMS; DRIVEN; EXISTENCE; STABILITY; DELAY; INCLUSIONS;

D O I：

10.1007/s41980-018-0043-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish sufficient conditions for exact null controllability of Sobolev type stochastic differential equations with fractional Brownian motion and Poisson jumps in Hilbert spaces, where the time fractional derivative is the Hilfer derivative. The exact null controllability result is derived by using fractional calculus, compact semigroup, fixed point theorem and stochastic analysis. Finally, an example is given to show the application of our results.

引用

页码：673 / 690

页数：18

共 42 条

[1]

Ahmed H. M., 2014, ADV DIFFER EQU-NY, V113, P1

[2] Hilfer fractional stochastic integro-differential equations [J].

Ahmed, Hamdy M. ;

El-Borai, Mahmoud M. .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 331 :182-189

[3] Controllability of fractional stochastic delay equations [J].

Ahmed H.M. .

Lobachevskii Journal of Mathematics, 2009, 30 (3) :195-202

[4]

[Anonymous], 2000, Applications of Fractional Calculus in Physics

[5]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[6] Existence and exponential stability for neutral stochastic integrodifferential equations with impulses driven by a fractional Brownian motion [J].

Arthi, G. ;

Park, Ju H. ;

Jung, H. Y. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 32 :145-157

[7] Sample controllability of nonlinear stochastic integrodifferential systems [J].

Balachandran, K. ;

Kim, J-H .

NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2010, 4 (03) :543-549

[8] Local null controllability of nonlinear functional differential systems in Banach space [J].

Balachandran, K ;

Balasubramaniam, P ;

Dauer, JP .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1996, 88 (01) :61-75

[9] Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficients [J].

Benchaabane, Abbes ;

Sakthivel, Rathinasamy .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 312 :65-73

[10] Impulsive neutral functional differential equations driven by a fractional Brownian motion with unbounded delay [J].

Boudaoui, Ahmed ;

Caraballo, Tomas ;

Ouahab, Abdelghani .

APPLICABLE ANALYSIS, 2016, 95 (09) :2039-2062

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