Geodesic
Inverse coefficient problem for a partial differential equation with multi-term orders fractional Riemann–Liouville derivatives
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 321-338

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This work studies direct initial boundary value and inverse coefficient determination problems for a one-dimensional partial differential equation with multi-term orders fractional Riemann–Liouville derivatives. The unique solvability of the direct problem is investigated and a priori estimates for its solution are obtained in weighted spaces, which will be used for studying the inverse problem. Then, the inverse problem is equivalently reduced to a nonlinear integral equation. The fixed-point principle is used to prove the unique solvability of this equation.
Keywords: fractional order equation, direct problem, inverse problem, Fourier method, Mittag–Leffler function, uniqueness
Mots-clés : Laplace transform, existence 
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     author = {D. K. Durdiev and I. I. Hasanov},
     title = {Inverse coefficient problem for a partial differential equation with multi-term orders fractional {Riemann{\textendash}Liouville} derivatives},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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D. K. Durdiev; I. I. Hasanov. Inverse coefficient problem for a partial differential equation with multi-term orders fractional Riemann–Liouville derivatives. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 321-338. http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a1/