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 diferential part, the problem is reduced to an integral equation with a kernel with a special function. Te special function is presented as a generalized hypergeometric function. Te 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]. Te results of the study remain unchanged. Te kernel of the integral equation is estimated. Conditions for the solvability of the integral equation are obtained.