Fractional diffusion equations interpolate between damping and waves

Abstract

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.

References in corpus (4)

• The Prabhakar or three parameter Mittag--Leffler function: theory and application
• A practical guide to Prabhakar fractional calculus
• Review of Some Promising Fractional Physical Models
• The generalized Cattaneo (telegrapher's) equation and corresponding random walks

Cited by in corpus (2)

• Bio-heat regimes in fractal-based models of tumors
• Schrödinger-invariance in the voter model