BVP with a Load in the Form of a Fractional Integral

M.T. Kosmakova, Dana M. Akhmanova, K.A. Izhanova

2024

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DOI 10.1155/2024/7034103

Data confidence 70 medium

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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.