Quantum mechanics

Context (archaeology)

Magnetic field

Power law

Statistics

Herschel–Bulkley fluid

Classical mechanics

Geology

Paleontology

Fractal

Physics

Mathematics

Laplace transform

Ferrofluid

Fractal dimension

Newtonian fluid

Non-Newtonian fluid

Mathematical analysis

Fractal analysis

Fractal derivative

Mechanics

Fractional calculus

European Journal of Mechanics - B/Fluids

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 Hα,β+11,αF. The Fox-H function Hα,β+11,αF 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.

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