The first boundary problem for heat conduction equation with a load of fractional order. II

Abstract

In this paper we consider the first boundary value problem for a loaded heat conduction equation in a quarter plane. A loaded summand is the trace of the derivative of fractional order on the manifold x=t. Solving of the problem is reduced to the study of singular Volterra integral equation of the second kind with incompressible kernel. Using the regularization method by solution of the characteristic equation it is shown that the singular Volterra integral equation have the nonempty spectrum 1/2≤β<1. Theorem on the existence of a nontrivial solution of the homogeneous boundary value problem in an unbounded domain is proved.