The objective of this research is to present new fixed point theorems for two separate families of fuzzy-dominated mappings. These mappings must satisfy a unique locally contraction in a complete b-multiplicative metric space. Also, we have obtained novel results for families of fuzzy-dominated mappings on a closed ball that meet the requirements of a generalized locally contraction. This research introduces new and challenging fixed-point problems for families of ordered fuzzy-dominated mappings in ordered complete b-multiplicative metric spaces. Moreover, we demonstrate a new concept for families of fuzzy graph-dominated mappings on a closed ball in these spaces. Additionally, we present novel findings for graphic contraction endowed with graphic structure. These findings are groundbreaking and provide a strong foundation for future research in this field. To demonstrate the uniqueness of our novel findings, we provide evidence of their applicability in obtaining the common solution of integral and fractional differential equations. Our findings have resulted in modifications to several contemporary and classical results in the research literature. This provides further evidence of the originality and impact of our work.

中文翻译：

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模糊主导映射的不同族的新颖结果满足 b 乘性度量空间中的高级局部收缩及其应用

本研究的目的是为两个独立的模糊支配映射族提出新的不动点定理。这些映射必须满足完整 b 乘法度量空间中的唯一局部收缩。此外，我们还获得了闭球上模糊主导映射族的新颖结果，满足广义局部收缩的要求。这项研究为有序完全 b 乘性度量空间中的有序模糊主导映射族引入了新的、具有挑战性的定点问题。此外，我们还展示了这些空间中封闭球上的模糊图主导映射族的新概念。此外，我们还提出了赋予图形结构的图形收缩的新发现。这些发现具有开创性，为该领域的未来研究奠定了坚实的基础。为了证明我们新发现的独特性，我们提供了它们在获得积分和分数微分方程的共同解方面的适用性的证据。我们的研究结果对研究文献中的一些当代和经典结果进行了修改。这进一步证明了我们工作的原创性和影响力。