The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators.

中文翻译：

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关于一个函数相对于另一个函数的加权分数运算符

本研究的主要目标是在某些空间上定义加权分数算子。我们首先证明加权积分在某些空间中有界。之后，我们讨论了在绝对类连续空间上定义的加权分数导数。最后，我们提出了一个改进的拉普拉斯变换，它可以完美地应用于这些算子。