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<p>A unique solvability of direct and inverse problems with dynamical conditions in space variables for a sub-diffusion equation involving the Hilfer-Prabhakar integral-differential operator has been proved. Proofs are done with the application of the spectral expansion method, based on the solution of the Cauchy problem for the corresponding fractional differential equation and using certain properties of the bivariate Mittag-Leffler function.</p>

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Direct and inverse problems with a dynamical condition for the sub-diffusion equation involving the Hilfer-Prabhakar integral-differential operator

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Erkinjon Karimov,
  • Sebti Kerbal,
  • Khurshidjon Turdiev

摘要

A unique solvability of direct and inverse problems with dynamical conditions in space variables for a sub-diffusion equation involving the Hilfer-Prabhakar integral-differential operator has been proved. Proofs are done with the application of the spectral expansion method, based on the solution of the Cauchy problem for the corresponding fractional differential equation and using certain properties of the bivariate Mittag-Leffler function.