Local solvability of the nonlinear inverse problem for the equation with Dzhrbashyan–Nersesyan derivatives
https://doi.org/10.25587/2411-9326-2025-2-90-91
Abstract
A class of nonlinear identification problems for differential equations in Banach spaces resolved with respect to the highest Dzhrbashyan — Nersesyan fractional derivative is investigated. The existence and the uniqueness of a local solution of the identification problem are proved by the method of contraction maps.
About the Authors
D. V. Melekhina
Chelyabinsk State University
Russian Federation
Russian Federation
Daria V. Melekhina, Mathematics Faculty, Mathematical Analysis Department
129 Kashirin Brothers Street, Chelaybinsk 454001
V. E. Fedorov
Chelyabinsk State University
Russian Federation
Russian Federation
Vladimir E. Fedorov, Mathematics Faculty, Mathematical Analysis Department
129 Kashirin Brothers Street, Chelaybinsk 454001
References
1. Джрбашян М. М., Нерсесян Ф. Б. Дробные производные и задача Коши для дифференциальных уравнений дробного порядка // Изв. Акад. Наук Арм. ССР. 1968. Т. 3, № 1. С. 3–28.
2. Fedorov V. E., Plekhanova M. V., Melekhina D. V. On local unique solvability for a class of nonlinear identification problems // Axioms. 2023. V. 12, N 11. P. 1013.
Review
For citations:
Melekhina D.V., Fedorov V.E. Local solvability of the nonlinear inverse problem for the equation with Dzhrbashyan–Nersesyan derivatives. Mathematical notes of NEFU. 2025;32(2):90-91. (In Russ.) https://doi.org/10.25587/2411-9326-2025-2-90-91
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