Abstract
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.
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