BVP with a Load in the Form of a Fractional Integral

Abstract

A boundary value problem for a nonhomogeneous heat equation with a load in the form of a fractional Riemann–Liouville integral of an order β∈0,1 is considered. By inverting the differential part, the problem is reduced to an integral equation with a kernel with a special function. The special function is presented as a generalized hypergeometric function. The limiting cases of the order β of the fractional derivative are studied: it is shown that the interval for changing the order of the fractional derivative can be expanded to integer values β∈0,1. The results of the study remain unchanged. The kernel of the integral equation is estimated. Conditions for the solvability of the integral equation are obtained.