In this paper, we intend to obtain some numerical approximations of inverse problem by means of fractional differential equations under interval uncertainty. For this purpose, using perturbed Collage theorem, we achieve the approximations with the help of minimization procedure. We discuss the Picard operator and the existence with the uniqueness of solutions of interval fractional differential equations (IFDEs) using contraction mappings. Some modifications of existing results on the approximations of interval-valued functions using Schauder basis in the metric space are derived. Then, the fractional version of approximation in the Banach space is obtained to compute the numerical solution. In fact, we also employ Collage-based method for solving IFDEs with inverse problem. Finally, illustrative examples are solved in details to show that the results are in good agreement with the exact solutions for different values of fractional order derivative under generalized differentiability.

在本文中，我们打算通过区间不确定性下的分数阶微分方程获得一些反问题的数值近似。为此，我们使用扰动的拼贴定理，借助最小化过程来实现近似。我们讨论使用收缩映射的Picard算子和区间分数阶微分方程（IFDE）解的唯一性。得出了在度量空间中使用Schauder基对区间值函数进行逼近的现有结果的一些修改。然后，获得Banach空间中逼近的分数形式以计算数值解。实际上，我们还采用基于拼贴的方法来求解具有反问题的IFDE。最后，