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A Class of Fractional Degenerate Evolution Equations with Delay

Author

Listed:
  • Amar Debbouche

    (Department of Mathematics, Guelma University, Guelma 24000, Algeria)

  • Vladimir E. Fedorov

    (Department of Mathematical Analysis, Chelyabinsk State University, 129 Kashirin Brothers St., Chelyabinsk 454001, Russia
    Laboratory of Functional Materials, South Ural State University (National Research University), Lenin Av. 76, Chelyabinsk 454080, Russia
    Department of Differential Equations, N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya St., Yekaterinburg 620108, Russia)

Abstract

We establish a class of degenerate fractional differential equations involving delay arguments in Banach spaces. The system endowed by a given background and the generalized Showalter–Sidorov conditions which are natural for degenerate type equations. We prove the results of local unique solvability by using, mainly, the method of contraction mappings. The obtained theory via its abstract results is applied to the research of initial-boundary value problems for both Scott–Blair and modified Sobolev systems of equations with delays.

Suggested Citation

  • Amar Debbouche & Vladimir E. Fedorov, 2020. "A Class of Fractional Degenerate Evolution Equations with Delay," Mathematics, MDPI, vol. 8(10), pages 1-8, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1700-:d:423349
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    References listed on IDEAS

    as
    1. Dumitru Baleanu & Vladimir E. Fedorov & Dmitriy M. Gordievskikh & Kenan Taş, 2019. "Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
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    Cited by:

    1. 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.

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