分数阶脉冲中立型随机微积分方程的适定性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (2): 405-421.

分数阶脉冲中立型随机微积分方程的适定性

Diem Dang Huan^1,2, 高洪俊¹

1. 南京师范大学数学科学学院数学研究所南京 210023;
2. 北江农林大学基础科学学院越南北江 21000

收稿日期:2013-07-12 修回日期:2014-04-28 出版日期:2015-04-25 发布日期:2015-04-25
作者简介:Diem Dang Huan,E-mail:diemdanghuan80@gmail.com;高洪俊,E-mail:gaohj@njnu.edu.cn
基金资助:
国家自然科学基金(11171158)和江苏省教育厅自然科学基金(11KJA110001)资助

Well-Posedness for Fractional Neutral Impulsive Stochastic Integro-Differential Equations

Diem Dang Huan^1,2, Gao Hongjun¹

1. School of Mathematical Science, Nanjing Normal University, Nanjing 210023;
2. Faculty of Basic Sciences, Bacgiang Agriculture and Forestry University, Bacgiang 21000, Vietnam

Received:2013-07-12 Revised:2014-04-28 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

利用 Sadovskii 不动点定理以及α-预解算子理论讨论了一类在 Hilbert 空间中带无限时滞的分数阶脉冲中立型随机微积分方程温和解的适定性, 并通过举例说明了结果的有效性.

关键词: α-预解算子, 分数阶随机微积分方程, 相空间, 中立型, 脉冲, Sadovskii不动点定理

Abstract:

This paper deals with the well-posedness of mild solutions for a class of fractional neutral impulsive stochastic integro-differential equations with infinite delay in Hilbert spaces. The results are obtained by using the Sadovskii fixed point theorem combined with theories of α-resolvent operators. An example is provided to illustrate the effectiveness of the proposed results.

Key words: α-Resolvent operator, Fractional stochastic integro-differential equations, Phase space, Neutral, Impulses, Sadovskii's fixed point theorem

中图分类号:

O211.63

Diem Dang Huan, 高洪俊. 分数阶脉冲中立型随机微积分方程的适定性[J]. 数学物理学报, 2015, 35(2): 405-421.

Diem Dang Huan, Gao Hongjun. Well-Posedness for Fractional Neutral Impulsive Stochastic Integro-Differential Equations[J]. Acta mathematica scientia,Series A, 2015, 35(2): 405-421.

参考文献

[1] Chang Y K, Nieto J J. Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators. Numer Funct Anal Optim, 2009, 30: 227-244

[2] Cuevas C, Hernández E, Rabelo M. The existence of solutions for impulsive neutral functional differential equations. Comput Math Appl, 2009, 58(4): 774-757

[3] Hernández E, Rabelo M, Henríquez H. Existence of solutions for impulsive partial neutral functional differential equations. J Math Anal Appl, 2007, 331(2): 1135-1158

[4] Yan Z M. Existence of solutions for nonlocal impulsive partial functional integrodifferential equations via fractional operators. J Comput Appl Math, 2011, 235(8): 2252-2262

[5] Hale J K, Kato J. Phase spaces for retarded equations with infinite delay. Funkcial Ekvac, 1978, 21: 11-41

[6] Hino Y, Murakami S, Naito T. Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics. Berlin: Springer-Verlag, 1991

[7] Hu L, Ren Y. Existence results for impulsive neutral stochastic functional integro-differential equations. Acta Appl Math, 2010, 111(3): 303-317

[8] Parthasarathy C, Arjunan M M. Existence results for impulsive neutral stochastic functional integrodifferential systems with infinite delay. Malaya J Matematik, 2012, 1(1): 26-41

[9] Hilfer R. Applications of Fractional Calculus in Physics. Singapore: World Scientific, 2000

[10] Lakshmikantham V, Leela S, Vasundhara Devi J. Theory of Fractional Dynamic Systems. Cambridge: Cambridge Scientific Publishers, 2009

[11] Agarwal R P, Dos Santos J P C, Cuevas C. Analytic resolvent operator and existence results for fractional integro-differential equations. J Abstr Differ Equ Appl, 2012, 2(2): 26-47

[12] Balachandran K, Kiruthika S, Trujillo J J. Existence results for fractional impulsive integrodifferential equations in Banach spaces. Commun Nonlinear Sci Numer Simul, 2011, 16(4): 1970-1977

[13] De Andrade B, Dos Santos J P C. Existence of solutions for a fractional neutral integro-differential equation with unbounded delay. Electr J Differ Equ, 2012, 90: 1-13

[14] Zhou Y, Jiao F. Existence of mild solutions for fractional neutral evolution equations. Comput Math Appl, 2010, 59: 1063-1077

[15] Cui J, Yan L T. Existence result for fractional neutral stochastic integro-differential equations with infinite delay. J Phys A: Math Theor, 2011, 44: 1-16

[16] Sakthivel R, Revathi P, Mahmudov N I. Asymptotic stability of fractional stochastic neutral differential equations with infinite delays. Abstr Appl Anal, 2013, Article ID 769257, 9 pages

[17] Da Prato G, Zabczyk J. Stochastic Equations in Infinite Dimensions. Cambridge: Cambridge University Press, 1992

[18] Dos Santos J P C, Cuevas C, De Andrade B. Existence results for a fractional equation with state-dependent delay. Adv Differ Equ, 2011, Article ID 642013, 15 pages

[19] Pazy A. Semigroup of Linear Operators and Applications to Partial Differential Equations. New York: Springer Verlag, 1992

[20] Yan Z M, Zhang H W. Existence of solutions to impulsive fractional partial neutral integro-differential inclusions equation with state-dependent delay. Electr J Differ Equa, 2013, 81: 1-21

[21] Sadovskii B N. On a fixed point principle. Funct Anal Appl, 1967, 1: 151-153

[22] Marle C M. Measures et Probabilités. Hermann, Paris, France: Ensei des Sci, 1974

[23] Hernández E, Rierri M, Goncalves G. Existence results for an impulsive abstract partial differential equation with state-dependent delay. Comput Math Appl, 2006, 52: 411-420