Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion

Entropy

关键词: fractional calculus;    non-Fourier heat conduction;    fractional diffusion-wave equation;    perfect thermal contact;    Laplace transform;    Mittag-Leffler function;    Wright function;    Mainardi function;   

DOI  :  10.3390/e15104122

来源: mdpi

【 摘 要 】

The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion and a matrix being in perfect thermal contact at is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional orde and respectively. The Laplace transform with respect to time is used. The approximate solution valid for small values of time is obtained in terms of the Mittag-Leffler, Wright, and Mainardi functions.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.