Fractional diffusion equations interpolate between damping and waves

Fractional diffusion equations interpolate between damping and waves

The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection–diffusion equation is also solved and an application to Pennes bioheat model is presented. Ge...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2024-09, Vol.57 (35), p.355202
Hauptverfasser: Manapany, Andy, Fumeron, Sébastien, Henkel, Malte
Format: Artikel
Sprache:eng
Schlagworte:
anomalous diffusion
biophysics
fractional calculus
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection–diffusion equation is also solved and an application to Pennes bioheat model is presented. Generically, a wave-like transport at short times passes over to a diffusion-like behaviour at later times.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ad6c02