Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficients

被引：57

作者：

Benchaabane, Abbes ^{[1
]}

Sakthivel, Rathinasamy ^{[2
]}

机构：

[1] Guelma Univ, Dept Math, Guelma 24000, Algeria

[2] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 312卷

关键词：

Stochastic differential equations of Sobolev-type; Existence and uniqueness; Fractional derivatives; Non-Lipschitz coefficients; EVOLUTION-EQUATIONS; NONLOCAL CONDITIONS; INTEGRODIFFERENTIAL EQUATIONS; APPROXIMATE CONTROLLABILITY; ROSENBLATT PROCESS; EXISTENCE; SYSTEMS; DELAY; INCLUSIONS; DRIVEN;

D O I：

10.1016/j.cam.2015.12.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates the existence and uniqueness of mild solutions for a class of nonlinear fractional Sobolev-type stochastic differential equations in Hilbert spaces. In this work, we used the fractional calculus, semigroup theory and stochastic analysis techniques for obtaining the required result. A new set of sufficient condition is established with the coefficients in the equations satisfying some non-Lipschitz conditions, which include classical Lipschitz conditions as special cases. More precisely, the results are obtained by means of standard Picard's iteration. Finally, an example is given to illustrate the obtained theory. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：65 / 73

页数：9

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