Inverse coefficient problem for a partial differential equation with multi-term orders fractional Riemann–Liouville derivatives

D. K. Durdiev   ; I. I. Hasanov

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 321-338

Résumé

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.

Détail

Keywords: fractional order equation, direct problem, inverse problem, Fourier method, Mittag–Leffler function, uniqueness
Mots-clés : Laplace transform, existence

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