Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficients
Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficients
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DOI：
10.1016/j.cam.2015.12.020
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
A. Benchaabane;R. Sakthivel
中科院分区：
文献类型：
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作者：
A. Benchaabane;R. Sakthivel
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.
