Geodesic
Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 355-367

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This article is devoted to the study of an inverse source problem for a mixed type equation with a fractional diffusion equation in the parabolic part and a wave equation in the hyperbolic part of a cylindrical domain. The solution is obtained in the form of Fourier–Bessel series expansion using an orthogonal set of Bessel functions. The theorems of uniqueness and existence of a solution are proved.
Keywords: inverse problem, equation of mixed type, Fourier–Bessel series, Mittag–Leffler function, uniqueness and existence. 
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     author = {D. K. Durdiev},
     title = {Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {355--367},
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     volume = {26},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a8/}
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D. K. Durdiev. Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 355-367. http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a8/