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http://dx.doi.org/10.18419/opus-12884
Autor(en): | Kleiner, Tillmann Hilfer, Rudolf |
Titel: | Fractional glassy relaxation and convolution modules of distributions |
Erscheinungsdatum: | 2021 |
Dokumentart: | Zeitschriftenartikel |
Seiten: | 29 |
Erschienen in: | Analysis and mathematical physics 11 (2021), No. 130 |
URI: | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-129037 http://elib.uni-stuttgart.de/handle/11682/12903 http://dx.doi.org/10.18419/opus-12884 |
ISSN: | 1664-2368 1664-235X |
Zusammenfassung: | Solving fractional relaxation equations requires precisely characterized domains of definition for applications of fractional differential and integral operators. Determining these domains has been a longstanding problem. Applications in physics and engineering typically require extension from domains of functions to domains of distributions. In this work convolution modules are constructed for given sets of distributions that generate distributional convolution algebras. Convolutional inversion of fractional equations leads to a broad class of multinomial Mittag-Leffler type distributions. A comprehensive asymptotic analysis of these is carried out. Combined with the module construction the asymptotic analysis yields domains of distributions, that guarantee existence and uniqueness of solutions to fractional differential equations. The mathematical results are applied to anomalous dielectric relaxation in glasses. An analytic expression for the frequency dependent dielectric susceptibility is applied to broadband spectra of glycerol. This application reveals a temperature independent and universal dynamical scaling exponent. |
Enthalten in den Sammlungen: | 08 Fakultät Mathematik und Physik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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s13324-021-00504-5.pdf | 634,4 kB | Adobe PDF | Öffnen/Anzeigen |
Diese Ressource wurde unter folgender Copyright-Bestimmung veröffentlicht: Lizenz von Creative Commons