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Degenerate Multi-Term Equations with Gerasimov–Caputo Derivatives in the Sectorial Case

Author

Listed:
  • Vladimir E. Fedorov

    (Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St. 129, 454001 Chelyabinsk, Russia)

  • Kseniya V. Boyko

    (Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St. 129, 454001 Chelyabinsk, Russia)

Abstract

The unique solvability for the Cauchy problem in a class of degenerate multi-term linear equations with Gerasimov–Caputo derivatives in a Banach space is investigated. To this aim, we use the condition of sectoriality for the pair of operators at the oldest derivatives from the equation and the general conditions of the other operators’ coordination with invariant subspaces, which exist due to the sectoriality. An abstract result is applied to the research of unique solvability issues for the systems of the dynamics and of the thermoconvection for some viscoelastic media.

Suggested Citation

  • Vladimir E. Fedorov & Kseniya V. Boyko, 2022. "Degenerate Multi-Term Equations with Gerasimov–Caputo Derivatives in the Sectorial Case," Mathematics, MDPI, vol. 10(24), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4699-:d:1000242
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    References listed on IDEAS

    as
    1. Amar Debbouche & Vladimir E. Fedorov, 2020. "A Class of Fractional Degenerate Evolution Equations with Delay," Mathematics, MDPI, vol. 8(10), pages 1-8, October.
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