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Lahmoudi Ahmed and Lakhel El Hassan, Retarded stochastic fractional neutral functional differential equations driven by Rosenblatt process with unbounded delay, Eur. J. Math. Appl. 2 (2022), Article ID 8.

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Volume 2 (2022), Article ID 8

https://doi.org/10.28919/ejma.2022.2.8

Published: 07/04/2022

Abstract:

Hermite processes are self-similar processes with stationary increments, the Hermite process of order $1$ is fractional Brownian motion and the Hermite process of order $2$ is the Rosenblatt process. In this paper, we consider a class of fractional neutral stochastic functional differential equations with infinite delay driven by Rosenblatt process with index $H\in (\frac{1}{2},1)$ which is a special case of a self-similar process with long-range dependence. More precisely, we prove the existence of mild solutions by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is provided to demonstrate the effectiveness of the theoretical result.

How to Cite:

Lahmoudi Ahmed and Lakhel El Hassan, Retarded stochastic fractional neutral functional differential equations driven by Rosenblatt process with unbounded delay, Eur. J. Math. Appl. 2 (2022), Article ID 8. https://doi.org/10.28919/ejma.2022.2.8