In this paper, we considered a complex real-world problem with existing mathematical equations. These equations were converted to fractional-stochastic differential and integral equations. Analysis of existence and uniqueness was presented for each case. Numerical simulations have been performed for different values of fractional orders and the density of randomness. We discuss in detail the results for the Caputo and Atangana-Baleanu case. The algorithm is given to obtain the numerical solution of each model. The numerical results are shown for the integer case, arbitrary derivative, and stochastic case. The results obtained indicated that this concept will open new doors of investigation toward modeling real-world problems.

在本文中，我们用现有的数学方程考虑了一个复杂的现实世界问题。这些方程被转换为分数随机微分方程和积分方程。对每个案例都进行了存在性和唯一性分析。已经针对不同的分数阶值和随机性密度进行了数值模拟。我们详细讨论了 Caputo 和 Atangana-Baleanu 案例的结果。给出算法以获得每个模型的数值解。数值结果显示为整数情况、任意导数和随机情况。获得的结果表明，这一概念将为模拟现实世界问题的研究打开新的大门。