In this paper we study existence and uniqueness of solution stochastic differential equations involving fractional integrals driven by Riemann-Liouville multifractional Brownian motion and a standard Brownian. Then, we obtain approximate numerical solution of our problem and colon cancer chemotherapy effect model are presented to confirm our results. We show that considering time dependent Hurst parameters play an important role to get more realistic results.

中文翻译：

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论多重分数阶随机时滞微分方程解的存在唯一性

在本文中，我们研究了由黎曼-刘维尔多重分数布朗运动和标准布朗运动驱动的涉及分数积分的随机微分方程解的存在性和唯一性。然后，我们获得了问题的近似数值解，并提出了结肠癌化疗效果模型来证实我们的结果。我们表明，考虑时间相关的赫斯特参数对于获得更现实的结果起着重要作用。