In this paper, we study a class of doubly perturbed uncertain differential equations driven by canonical process that is the counterpart of Wiener process in the framework of uncertain theory. We give some sufficient conditions for the existence and uniqueness of solutions of the present problem under some weak conditions, where a convex combination of the Nagumo and Osgood conditions is considered. Subsequently, we consider the stability properties with regard to the initial value and coefficients. Finally, an example is provided to illustrate the effectiveness of our main results.

中文翻译：

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双摄动不确定微分方程


在本文中，我们研究了一类由正则过程驱动的双扰动不确定微分方程，该正则过程是不确定理论框架中维纳过程的对应部分。我们给出了一些弱条件下当前问题解的存在性和唯一性的充分条件，其中考虑了Nagumo 和Osgood 条件的凸组合。随后，我们考虑初始值和系数的稳定性。最后，提供了一个例子来说明我们主要结果的有效性。