Fractional heat conduction in an infinite medium with a spherical inclusion

Abstract

The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion (0 < r < R) anda matrix (R < r < ∞) being in perfect thermal contact at r = R is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 0 < 2 and 0 < β < 2, 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 ©2013 by the authors; licensee MDPI, Basel, Switzerland.