Geodesic
Nonlocal problem for a fractional-order mixed-type equation with involution
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 55-65

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In this paper, we examine the unique solvability of a nonlocal problem for a nonlocal analog of a mixed parabolic-hyperbolic equation with a generalized Riemann–Liouville operator and involution with respect to the space variable. A criterion for the uniqueness of the solution is established and sufficient conditions for the unique solvability of the problem are determined. By the method of separation of variables, a solution is constructed in the form of an absolutely and uniformly convergent series with respect to eigenfunctions of the corresponding one-dimensional spectral problem. The stability of the solution of the problem under consideration under a nonlocal condition is established.
Keywords: mixed-type equation, equation with involution, nonlocal problem, nonlocal differential equation, gluing conditions, Hilfer operator, Mittag-Leffler function, Fourier series. 
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     author = {B. J. Kadirkulov and G. A. Kayumova},
     title = {Nonlocal problem for a fractional-order mixed-type equation with involution},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {55--65},
     publisher = {mathdoc},
     volume = {210},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_210_a6/}
}
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B. J. Kadirkulov; G. A. Kayumova. Nonlocal problem for a fractional-order mixed-type equation with involution. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 55-65. http://geodesic.mathdoc.fr/item/INTO_2022_210_a6/