Geodesic
On the solvability of an integral equation associated with the fractional loaded heat conduction problem
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 27-36

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In this paper, we examine a one-dimensional boundary-value problem for the heat equation with a loaded term in the form of the Caputo fractional derivative with respect to a spatial variable. The problem is reduced to the Volterra integral equation with a kernel containing a Wright-type function, for which solvability conditions are obtained.
Keywords: loaded heat equation, fractional derivative, Volterra integral equation, Wright-type function 
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M. T. Kosmakova; A. N. Khamzeeva. On the solvability of an integral equation associated with the fractional loaded heat conduction problem. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 27-36. http://geodesic.mathdoc.fr/item/INTO_2024_233_a2/