In this paper, we study the fractional integro-differential equation under the notion of fuzziness. We consider the fuzzy fractional Volterra-Fredholm integro-differential equation in the Caputo sense and show its existence and uniqueness by using fixed point theory. Further, we use the modified Adomian decomposition method (MADM) to determine the solution of the proposed problem. We provide some examples to support our method. We also provide graphical representation to visualize the behavior of the solutions. At the end of the paper, we present the conclusion part.

中文翻译：

---

模糊分数阶Volterra-Fredholm积分微分方程的分析

在本文中，我们研究了模糊概念下的分数阶积分微分方程。我们在卡普托意义上考虑了模糊分数阶Volterra-Fredholm积分微分方程，并通过不动点理论证明了其存在性和唯一性。此外，我们使用改进的Adomian分解方法（MADM）来确定所提出问题的解决方案。我们提供一些示例来支持我们的方法。我们还提供图形表示形式以可视化解决方案的行为。在本文的最后，我们介绍了结论部分。