Newtonsche Aufheizung, Abelsche Integralgleichungen zweiter Art und Mittag-Leffler-Funktionen

The problem of heating a homogeneous half-space by radiation from outside across the plane boundary is considered. Newtonian heating means that the heat flux across the boundary is proportional to the difference of outside temperature and interior boundary temperature. The outside temperature is assumed to be constant and positive, the initial inside temperature is zero everywhere. The problem is onedim ensional in space. The temporal evolution of the inward boundary temperature obeys an Abel integral equation of second kind for whose explicit solution three methods are described (one by Laplace transform , the other two by infinite series defining the Mittag-Leffler function of index 1/2). The explicit solution facilitates discussion of its qualitative properties. Finally, the general Abel integral equation of second kind is treated by Mittag-Leffler functions.