Magnetic field diffusion in ferromagnetic materials: fractional calculus approaches

IF 2.2 Q1 MATHEMATICS, APPLIED
J. Hristov
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引用次数: 5

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.
铁磁材料中的磁场扩散:分数阶演算方法
本文讨论了磁场穿透铁磁材料的扩散近似,重点介绍了分数阶微积分的应用和相关的近似解。在场无关和场相关磁扩散率的情况下,开发了时间分数半导数和奇异核模型(Caputo时间分数算子)的应用实例:Dirichlet问题和时间相关边界条件(幂律斜坡)。应用积分平衡法和未指定指数的抛物线形,得到了上述情况的近似解。两种版本的积分方法已经成功实现:SDIM(单积分适用于时间分数半导数模型)和DIM(双积分模型适用于分数化奇异记忆模型)。讨论了因果概念意义上的衰退记忆方法和记忆核效应对模型构建的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.30
自引率
6.20%
发文量
13
审稿时长
16 weeks
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