Geodesic
On the well-posedness of an inverse problem for a degenerate evolutionary equation with the Dzhrbashyan--Nersesyan fractional derivative
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 80-88

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In this paper, we find necessary and sufficient conditions for the well-posedness of linear inverse coefficient problems for degenerate evolutionary equations with the Dzhrbashyan–Nersesyan fractional derivative in Banach spaces. We examine an inverse problem with a constant unknown coefficient under the generalized Showalter–Sidorov conditions and the condition of $p$-boundedness of a pair of operators in it. The general result is applied to the inverse problem for the system of dynamics of a viscoelastic Kelvin–Voigt fluid with the Dzhrbashyan–Nersesyan fractional derivative in time.
Keywords: fractional differential equation, fractional Dzhrbashyan–Nersesyan derivative, degenerate evolution equation
Mots-clés : inverse coefficient problem. 
@article{INTO_2022_213_a7,
     author = {M. V. Plekhanova and E. M. Izhberdeeva},
     title = {On the well-posedness of an inverse problem for a degenerate evolutionary equation with the  {Dzhrbashyan--Nersesyan} fractional derivative},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {80--88},
     publisher = {mathdoc},
     volume = {213},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_213_a7/}
}
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M. V. Plekhanova; E. M. Izhberdeeva. On the well-posedness of an inverse problem for a degenerate evolutionary equation with the  Dzhrbashyan--Nersesyan fractional derivative. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 80-88. http://geodesic.mathdoc.fr/item/INTO_2022_213_a7/