Geodesic
Inner boundary value problem with an integral condition for fractional diffusion equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 37 (2021) no. 4, pp. 24-29

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In this paper, we consider a nonlocal interior boundary value problem for the fractional diffusion equation with a fractional differentiation operator in the sense of Riemann-Liouville with integral conditions. The problem under study is equivalently reduced to a system of two Volterra integral equations of the second kind. The theorem of existence and uniqueness of the solution of the posed problem is proved.
Mots-clés : fractional diffusion equation
Keywords: Riemann — Liouville operator, Green's function, integral condition. 
@article{VKAM_2021_37_4_a2,
     author = {F. M. Losanova},
     title = {Inner boundary value problem with an integral condition for fractional diffusion equation},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {24--29},
     publisher = {mathdoc},
     volume = {37},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2021_37_4_a2/}
}
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F. M. Losanova. Inner boundary value problem with an integral condition for fractional diffusion equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 37 (2021) no. 4, pp. 24-29. http://geodesic.mathdoc.fr/item/VKAM_2021_37_4_a2/