5Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 119, pp. 1-15.

Title: Neutral  stochastic  partial functional integro-differential equations
       driven by G-Brownian motion 

Authors: Bingjun Wang
         Hongjun Gao

Abstract:
 In this article, we define the Hilbert-valued stochastic calculus with respect to 
 G-Brownian motion in G-framework. On that basis, we prove the existence and 
 uniqueness of mild solution for a class of neutral stochastic  partial functional 
 integro-differential equations  driven by G-Brownian motion with non-Lipschitz
 coefficients. Our results are established by means of the Picard approximation. 
 Moreover, we establish the stability of  mild solution. An example is given to 
 illustrate the theory.

Submitted December 14, 2018. Published November 15, 2019.
Math Subject Classifications: 60H15, 60H20, 34K50, 93E03.
Key Words: Neutral equation; G-Brownian motion; mild solution; stability.