2020/09/06 by A.R. Ashurov, Ashurov, A. R., Р.Т. Зуннунов +1
Computer Science · Mathematics · #35615 #35L35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2009.02712
openalex publication_date 2020/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An initial-boundary value problem for a subdiffusion equation with an elliptic operator A(D) in ℝN is considered. The existence and uniqueness theorems for a solution of this problem are proved by the Fourier method. Considering the order of the Caputo time-fractional derivative as an unknown parameter, the corresponding inverse problem of determining this order is studied. It is proved, that the Fourier transform of the solution u(ξ, t) at a fixed time instance recovers uniquely the unknown parameter. Further, a similar initial-boundary value problem is investigated in the case when operator A(D) is replaced by its power Aσ. Finally, the existence and uniqueness theorems for a solution of the inverse problem of determining both the orders of fractional derivatives with respect to time and the degree σ are proved. We also note that when solving the inverse problems, a decrease in the parameter ρ of the Mettag-Leffler functions Eρ has been proved.