Role of fractal-fractional derivative on ferromagnetic fluid via fractal Laplace transform: A first problem via fractal-fractional differential operator

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-fractional derivative 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 H-alpha,beta+1(1,alpha) (F). The Fox-H function H-alpha,beta+1(1,alpha) (F) 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. (C) 2020 Elsevier Masson SAS. All rights reserved.

Automated summary

The deformity of the magnetic field reveals different patterns of accumulation of particles in ferrofluid, leading to the existence of a homogeneous ferromagnetic liquid. A mathematical model incorporating fractal-fractional derivatives and Laplace transforms is developed to study the behavior of ferrofluid within porous media. The study demonstrates novel behaviors of velocity fields and highlights the lack of previous research on fractal-fractional derivatives in ferrofluid.