Inverse problem of determining an order of the Riemann-Liuville\n time-fractional derivative

2021/07/28 by Shavkat Alimov, Alimov, Shavkat, Ravshan Ashurov +1
Computer Science · Mathematics · #35R11 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2108.05201

openalex publication_date 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The inverse problem of determining the order of the fractional Riemann-\nLiouville derivative with respect to time in the subdi_usion equation with an\narbitrary positive self-adjoint operator having a discrete spectrum is\nconsidered. Using the classical Fourier method it is proved, that the value of\nthe norm jju(t)jj of the solution at a_xed time instance recovers uniquely the\norder of derivative. A list of examples is discussed, including a linear system\nof fractional di_erential equations, di_erential models with involution,\nfractional Sturm-Liouville operators, and many others.\n

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