分数阶扩散方程在阻尼与波动之间的插值
Fractional diffusion equations interpolate between damping and waves
AI总结：
本文研究了基于Caputo导数的时间分数阶扩散方程解的行为，分析了其对分数阶指数的依赖性，求解了对流扩散方程并应用于Pennes生物热模型，发现短时类波输运会过渡到长时类扩散行为。
摘要：
研究了基于Caputo导数的时间分数阶扩散方程解的行为，并分析了其对分数阶指数的依赖性。还求解了时间分数阶对流扩散方程，并展示了其在Pennes生物热模型中的应用。通常，短时间的类波输运会过渡到较晚时间的类扩散行为。
英文摘要：
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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