The Cattaneo type space-time fractional heat conduction equation

被引：35

作者：

Atanackovic, Teodor ^{[2
]}

Konjik, Sanja ^{[3
]}

Oparnica, Ljubica ^{[4
]}

Zorica, Dusan ^{[1
]}

机构：

[1] Serbian Acad Arts & Sci, Math Inst, Beograd 11000, Serbia

[2] Univ Novi Sad, Fac Tech Sci, Dept Mech, Novi Sad 21000, Serbia

[3] Univ Novi Sad, Fac Sci, Dept Math & Informat, Novi Sad 21000, Serbia

[4] Univ Novi Sad, Fac Educ, Sombor 25000, Serbia

来源：

CONTINUUM MECHANICS AND THERMODYNAMICS | 2012年 / 24卷 / 4-6期

关键词：

Caputo fractional derivative; Cattaneo heat conduction (diffusion) model; Laplace and Fourier transform; Generalized functions; DISTRIBUTED-ORDER; ANOMALOUS TRANSPORT; DIFFUSION-EQUATIONS; ENTROPY PRODUCTION; WAVES; SOUND;

D O I：

10.1007/s00161-011-0199-4

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

The classical heat conduction equation is generalized using a generalized heat conduction law. In particular, we use the space-time Cattaneo heat conduction law that contains the Caputo symmetrized fractional derivative instead of gradient and fractional time derivative instead of the first order partial time derivative . The existence of the unique solution to the initial-boundary value problem corresponding to the generalized model is established in the space of distributions. We also obtain explicit form of the solution and compare it numerically with some limiting cases.

引用

页码：293 / 311

页数：19

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