# Fractional neutral stochastic differential equations driven by $\alpha$-stable process

Volume 10, Issue 9, pp 4713--4723
Publication Date: September 09, 2017 Submission Date: March 01, 2016
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### Authors

Zhi Li - School of Information and Mathematics, Yangtze University, Jingzhou 434023, China.

### Abstract

In this paper, we are concerned with a class of fractional neutral stochastic partial differential equations driven by $\alpha$-stable process. By the stochastic analysis technique, the properties of operator semigroup and combining the Banach fixed-point theorem, we prove the existence and uniqueness of the mild solutions to this kind of equations driven by $\alpha$-stable process. In the end, an example is given to demonstrate the theory of our work.

### Share and Cite

##### ISRP Style

Zhi Li, Fractional neutral stochastic differential equations driven by $\alpha$-stable process, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4713--4723

##### AMA Style

Li Zhi, Fractional neutral stochastic differential equations driven by $\alpha$-stable process. J. Nonlinear Sci. Appl. (2017); 10(9):4713--4723

##### Chicago/Turabian Style

Li, Zhi. "Fractional neutral stochastic differential equations driven by $\alpha$-stable process." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4713--4723

### Keywords

• Fractional neutral SDEs
• $\alpha$-stable process
• existence and uniqueness.

•  60H15
•  60G15
•  60H05

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