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Inverse Problem of Determining the Kernel of Integro-Differential Fractional Diffusion Equation in Bounded Domain

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Abstract

In this paper, an inverse problem of determining a kernel in a one-dimensional integro-differential time-fractional diffusion equation with initial-boundary and overdetermination conditions is investigated. An auxiliary problem equivalent to the problem is introduced first. By Fourier method this auxilary problem is reduced to equivalent integral equations. Then, using estimates of the Mittag–Leffler function and successive aproximation method, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown kernel which will be used in study of inverse problem. The inverse problem is reduced to the equivalent integral equation. For solving this equation the contracted mapping principle is applied. The local existence and global uniqueness results are proven.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, 100170, Tashkent, Uzbekistan

    D. K. Durdiev & J. J. Jumaev

  2. Bukhara State University, 200118, Bukhara, Uzbekistan

    D. K. Durdiev & J. J. Jumaev

Authors
  1. D. K. Durdiev
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  2. J. J. Jumaev
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Correspondence to D. K. Durdiev or J. J. Jumaev.

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Durdiev, D.K., Jumaev, J.J. Inverse Problem of Determining the Kernel of Integro-Differential Fractional Diffusion Equation in Bounded Domain. Russ Math. 67, 1–13 (2023). https://doi.org/10.3103/S1066369X23100043

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