Geodesic
Boundary-value problem with an integral conjugation condition for a partial differential equation with the fractional Riemann--Liouville derivative that describes gas flows in a channel surrounded by a porous medium
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 66-76

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A boundary-value problem with an integral conjugation condition for a mixed equation with a fractional integro-differential operator was examined. The main result of the work is the proof of the unique solvability of the boundary-value problem with an integral conjugation condition for the equation consisting of two partial differential equations with the fractional Riemann–Liouville derivative in a rectangular domain. The problem is reduced to a Volterra integral equation of the second kind. The special role of the conjugation condition in the solvability of the problem is shown.
Keywords: boundary-value problem, integral conjugation condition, mixed fractional-order equation, gas flow in a channel. 
@article{INTO_2022_210_a7,
     author = {A. K. Urinov and E. T. Karimov and S. Kerbal},
     title = {Boundary-value problem with an integral conjugation condition for a partial differential equation with the fractional {Riemann--Liouville} derivative that describes gas flows in a channel surrounded by a porous medium},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {66--76},
     publisher = {mathdoc},
     volume = {210},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_210_a7/}
}
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A. K. Urinov; E. T. Karimov; S. Kerbal. Boundary-value problem with an integral conjugation condition for a partial differential equation with the fractional Riemann--Liouville derivative that describes gas flows in a channel surrounded by a porous medium. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 66-76. http://geodesic.mathdoc.fr/item/INTO_2022_210_a7/