A deformity of magnetic field discloses that different particle of ferrofluid exhibits different pattern to accumulate more closely with strong magnetic properties; this is because of the existence of a homogeneous ferromagnetic liquid. In this context, the Newtonian fluid (ordinary liquid) is magnetized by dispersing into porous media. A mathematical model for ferromagnetic fluid is developed by means of fractal–fractionalderivative based on the power law. A powerful technique of Laplace transform is invoked on the fractal-fractionalized MHD Newtonian fluid model embedded in porous medium based within power law kernel. The solution is investigated for velocity field by particularizing the format of mathematical special function so called Fox-H function ${\mathit{H}}_{\alpha ,\beta +1}^{1,\alpha }\left(F\right)$. The Fox-H function ${\mathit{H}}_{\alpha ,\beta +1}^{1,\alpha }\left(F\right)$ is employed among solution for the elimination of gamma functions. In order to generate the physical insight of fractal-fractionalized ferrofluid, a novel behaviors of velocity field based on the power law has disclosed several similarities and differences through the embedded rheological parameters. In short, It is worth noting that there is no previous paper related to ferrofluid involved with fractal–fractional​ derivative based on the power law.

磁场的变形表明，不同的铁磁流体颗粒表现出不同的模式以更紧密地聚集，具有很强的磁性。这是因为存在均匀的铁磁液体。在这种情况下，牛顿流体（普通液体）通过分散到多孔介质中而被磁化。通过基于幂定律的分形-分数导数建立了铁磁流体的数学模型。拉普拉斯变换的一项强大技术是基于幂律内核中嵌入在多孔介质中的分形-分形MHD牛顿流体模型。通过具体化称为Fox- H函数的数学特殊函数的格式来研究速度场的解决方案${\mathit{H}}_{\alpha ，\beta +\mathrm{1个}}^{\mathrm{1个}，\alpha }\left(F\right)$。Fox- H功能${\mathit{H}}_{\alpha ，\beta +\mathrm{1个}}^{\mathrm{1个}，\alpha }\left(F\right)$在解决方案中采用了来消除伽马功能。为了产生分形的铁磁流体的物理见解，基于幂定律的速度场的新行为通过嵌入的流变参数揭示了一些相似之处和不同之处。简而言之，值得注意的是，基于幂定律，以前没有关于铁磁流体涉及分形-分形导数的文章。