Fractional diffusion equations interpolate between damping and waves

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-21 DOI:10.1088/1751-8121/ad6c02
Andy Manapany, Sébastien Fumeron, Malte Henkel
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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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分数扩散方程在阻尼和波浪之间进行插值
研究了基于卡普托导数的时间分数扩散方程的解的行为,并分析了其对分数指数的依赖性。此外,还求解了时间分数对流扩散方程,并介绍了该方程在 Pennes 生物热模型中的应用。一般来说,短时间内的波状传输会在后期转变为扩散行为。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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