1. BVP with a Load in the Form of a Fractional Integral.
- Author
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Kosmakova, Minzilya, Akhmanova, Danna, Izhanova, Kamila, and Elgindy, Kareem T.
- Subjects
- *
BOUNDARY value problems , *FRACTIONAL integrals , *INTEGRAL equations , *HYPERGEOMETRIC functions , *SPECIAL functions - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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