The aim of this paper is to establish some fixed point and common fixed point theorems for $(\psi -\phi )$-almost weak contractions in complete S-metric spaces, followed by some supportive examples. Our results extend and generalize several results existing in the literature. We employ the outcomes of the fixed point theorems to establish the existence and uniqueness of a solution for a class of conformable differential equations which is a new branch of fractional calculus.

中文翻译：

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S-度量空间中\（（\ psi- \ phi）\） -几乎弱收缩的一些不动点定理

本文的目的是为$（\ psi-\ phi）$-完全S度量空间中的几乎弱收缩建立一些不动点定理和公共不动点定理，然后给出一些支持性的例子。我们的结果扩展并归纳了文献中已有的几种结果。我们利用不动点定理的结果来建立一类适形微分方程式的解的存在性和唯一性，这是分数阶微积分的一个新分支。