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

被引：0
作者：
Hamdy M. Ahmed
JinRong Wang
机构：
[1] El-Shorouk Academy,Department of Physics and Engineering Mathematics, Higher Institute of Engineering
[2] Guizhou University,Department of Mathematics
[3] Qufu Normal University,School of Mathematical Sciences
来源：
Bulletin of the Iranian Mathematical Society | 2018年 / 44卷
关键词：
Sobolev type stochastic differential equations; Fractional Brownian motion; Poisson jumps; Hilfer fractional derivative; Exact null controllability.; 34A08; 60H10; 93B05; 60G22; 60J75;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：673 / 690
页数：17
相关论文
共 82 条
  • [1] Mandelbrot BB(1968)Fractional Brownian motion, fractional noises and applications SIAM Rev. 10 422-473
  • [2] Van Ness JW(2000)Stieltjes integrals of Hilder continuous functions with applications to fractional Brownian motion J. Stat. Phys. 100 1049-1069
  • [3] Ruzmaikina A(2012)Mackey-Glass equation driven by fractional Brownian motion Phys. A Stat. Mech. Appl. 391 5465-5472
  • [4] Nguyen DT(2011)Positive solutions for a nonlocal fractional differential equation Nonlinear Anal. 74 3599-3605
  • [5] Wang Y(2012)Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives Appl. Math. Comput. 219 1420-1433
  • [6] Liu L(2018)Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations Appl. Math. Comput. 324 254-265
  • [7] Wu Y(2009)Stochastic calculus for fractional Brownian motion with Hurst exponent Ann. Probab. 37 565-614
  • [8] Zhang X(2015) a rough path method by analytic extension Stochastics 87 1061-1093
  • [9] Liu L(2016)Existence and global attractiveness of a pseudo almost periodic solution in p-th mean sense for stochastic evolution equation driven by a fractional Brownian motion Appl. Anal. 95 2039-2062
  • [10] Wu Y(2017)Impulsive neutral functional differential equations driven by a fractional Brownian motion with unbounded delay Appl. Math. Comput. 305 299-307
123456789