A Tracing of the Fractional Temperature Field

Abstract

This note is devoted to a study of $L^q$-tracing of the fractional temperature field $u(t,x)$ -- the weak solution of the fractional heat equation $(\partial_t+(-\Delta_x)^\alpha)u(t,x)=g(t,x)$ in $L^p(\mathbb R^{1+n}_+)$ subject to the initial temperature $u(0,x)=f(x)$ in $L^p(\mathbb R^n)$.