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Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives

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Listed:
  • Vladimir E. Fedorov

    (Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers Str. 129, 454001 Chelyabinsk, Russia
    Laboratory of Functional Materials, South Ural State University, Lenin Av. 76, 454080 Chelyabinsk, Russia)

  • Wei-Shih Du

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan)

  • Marko Kostić

    (Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia)

  • Aliya A. Abdrakhmanova

    (Department of Mathematics, Ufa State Aviation Technical University, Karl Marks Str. 12, 450077 Ufa, Russia)

Abstract

Some new necessary and sufficient conditions for the existence of analytic resolving families of operators to the linear equation with a distributed Riemann–Liouville derivative in a Banach space are established. We study the unique solvability of a natural initial value problem with distributed fractional derivatives in the initial conditions to corresponding inhomogeneous equations. These abstract results are applied to a class of initial boundary value problems for equations with distributed derivatives in time and polynomials with respect to a self-adjoint elliptic differential operator in spatial variables.

Suggested Citation

  • Vladimir E. Fedorov & Wei-Shih Du & Marko Kostić & Aliya A. Abdrakhmanova, 2022. "Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives," Mathematics, MDPI, vol. 10(5), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:681-:d:755950
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    References listed on IDEAS

    as
    1. Vladimir E. Fedorov, 2020. "Generators of Analytic Resolving Families for Distributed Order Equations and Perturbations," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
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