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<p>The problems of local unique solvability in the sense of generalized and in the sense of smooth solutions of nonlinear inverse problems for equations in Banach spaces with several fractional derivatives and Riemann–Liouville integrals are investigated. The operator in the linear part is assumed to generate an analytic resolving family of operators of the corresponding linear equation in the sector, the unknown coefficients in the equation depend on time. The conditions for the unique solvability of the inverse problem in a Banach space are used in the study of one class of initial-boundary value problems for a loaded fractional diffusion equation with several derivatives and Riemann–Liouville integrals with respect to time and unknown coefficients, with integral overdetermination conditions. Bibliography: 29 titles.</p>

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NONLINEAR INVERSE PROBLEMS FOR A CLASS OF EQUATIONS WITH RIEMANN–LIOUVILLE DERIVATIVES

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • V. E. Fedorov,
  • L. V. Borel,
  • N. D. Ivanova

摘要

The problems of local unique solvability in the sense of generalized and in the sense of smooth solutions of nonlinear inverse problems for equations in Banach spaces with several fractional derivatives and Riemann–Liouville integrals are investigated. The operator in the linear part is assumed to generate an analytic resolving family of operators of the corresponding linear equation in the sector, the unknown coefficients in the equation depend on time. The conditions for the unique solvability of the inverse problem in a Banach space are used in the study of one class of initial-boundary value problems for a loaded fractional diffusion equation with several derivatives and Riemann–Liouville integrals with respect to time and unknown coefficients, with integral overdetermination conditions. Bibliography: 29 titles.