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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2021 / Cilt: 11 - Sayı: 3

Magnetic field diffusion in ferromagnetic materials: fractional calculus approaches

Jordan HRISTOV
Pages
1–15
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The fading memory approach in the sense of the causality concept and memory kernel effect on the model constructions have been discussed.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The paper addresses diffusion approximations of magnetic field penetration of ferromagnetic materials with emphasis on fractional calculus applications and relevant approximate solutions.
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Key Findings & Data: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).
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Conclusion & Impact:The fading memory approach in the sense of the causality concept and memory kernel effect on the model constructions have been discussed.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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 timefractional 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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Cite This Article

HRISTOV, J. (2022). Magnetic field diffusion in ferromagnetic materials: fractional calculus approaches. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 11 - Sayı: 3, 1–15. https://ajindex.com/articles/440533

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