Magnetic field diffusion in ferromagnetic materials:   fractional calculus approaches

Jordan Hristov

doi:10.11121/ijocta.01.2021.001100

Authors

Jordan Hristov Department of Chemical Engineering,University of Chemical Technology and MetallurgySofia, Bulgaria https://orcid.org/0000-0002-7957-8192

DOI:

https://doi.org/10.11121/ijocta.01.2021.001100

Keywords:

Magnetic field, Diffusion approximation, Fractional calculus, Integral method, Memory kernel effect

Abstract

The paper addresses diffusion approximations of magnetic field penetration of ferromagnetic materials with emphasis on fractional calculus applications and relevant approximate solutions. Examples with applications of time-fractional semi-derivatives and singular kernel models (Caputo time fractional operator) in cases of field independent and field-dependent magnetic diffusivities have been developed: Dirichlet problems and time-dependent boundary condition (power-law ramp). Approximate solutions in all theses case have been developed by applications of the integral-balance method and assumed parabolic profile with unspecified exponents. Tow version of the integral method have been successfully implemented: SDIM (single integration applicable to time-fractional semi-derivative model) and DIM (double-integration model to fractionalized singular memory models). The fading memory approach in the sense of the causality concept and memory kernel effect on the model constructions have been discussed.

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Author Biography

Jordan Hristov, Department of Chemical Engineering,University of Chemical Technology and MetallurgySofia, Bulgaria

is a Professor of Chemical Engineering. His areas of interest are Transport Phenomena, Mathematical Modelling, Fractional Calculus, Heat Transfer, Approximate analytical methods, Dimensional analysis. With 185 research papers in various journals of high repute and listed by Web of Science he got total citations more than 2150 with h-index of 22 (Web of Science). In 2020 he was enlisted in the Stanford list of highly cited scholars among the first percent (at 318 position in Chemical Engineering). Professor Jordan Hristov is a Member of Editorial Boards of: Thermal Science, Particuology, Fractal and Fractional, Progress in Fractional Differentiations and Applications. The principle direction of his research in the last decade is related to approximate analytical solutions of non-linear and fractional problems, applications of non-singular fractional operator to non-local problems, fractional viscoelasticity, heat conduction, non-linear diffusion.

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