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Fractionalization of the Maxwell system was started with the constitutive equations. Relying on hereditary interrelations between characteristics of the electromagnetic field in a matter (see Sect. 1.2.5 of Vol. I) \(\textbf{D}(t) = \int _{-\infty }^{t} \phi (t-\tau ) \textbf{E}(\tau )d\tau ,\) \(\textbf{B}(t) = \int _{-\infty }^{t} \psi (t-\tau ) \textbf{H}(\tau ) d\tau ,\) Westerlund [143] chosen the kernels in a power form, \(\textbf{D}(t) = \varepsilon \frac{1}{\varGamma (-\nu )} \int _{-\infty }^{t} (t-\tau )^{-\nu -1} \textbf{E}(\tau )d\tau = \varepsilon _{-\infty } \textsf{D}^{\nu }_t \textbf{E}(t)\) .

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Electrodynamics

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  • 发表日期：

    2025年

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  • Vladimir V. Uchaikin

摘要

Fractionalization of the Maxwell system was started with the constitutive equations. Relying on hereditary interrelations between characteristics of the electromagnetic field in a matter (see Sect. 1.2.5 of Vol. I) \(\textbf{D}(t) = \int _{-\infty }^{t} \phi (t-\tau ) \textbf{E}(\tau )d\tau ,\) \(\textbf{B}(t) = \int _{-\infty }^{t} \psi (t-\tau ) \textbf{H}(\tau ) d\tau ,\) Westerlund [143] chosen the kernels in a power form, \(\textbf{D}(t) = \varepsilon \frac{1}{\varGamma (-\nu )} \int _{-\infty }^{t} (t-\tau )^{-\nu -1} \textbf{E}(\tau )d\tau = \varepsilon _{-\infty } \textsf{D}^{\nu }_t \textbf{E}(t)\) .