Time-fractional heat conduction in an infinite plane containing an external crack under heat flux loading

Abstract

The time-fractional heat conduction equation with the Caputo derivative is solved for an infinite plane with an external half-infinite crack which surfaces are exposed to the heat flux loading. The solution is obtained using the integral transform technique and is expressed in terms of the Mittag-Leffler function. The stress intensity factor is calculated for different values of the order of fractional derivative. Numerical results are illustrated graphically.