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

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.