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Generators of Analytic Resolving Families for Distributed Order Equations and Perturbations

Author

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  • Vladimir E. Fedorov

    (Department of Mathematical Analysis, Chelyabinsk State University, 454001 Chelyabinsk, Russia
    Laboratory of Functional Materials, South Ural State University, 454080 Chelyabinsk, Russia
    Department of Differential Equations, N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, 620108 Yekaterinburg, Russia)

Abstract

Linear differential equations of a distributed order with an unbounded operator in a Banach space are studied in this paper. A theorem on the generation of analytic resolving families of operators for such equations is proved. It makes it possible to study the unique solvability of inhomogeneous equations. A perturbation theorem for the obtained class of generators is proved. The results of the work are illustrated by an example of an initial boundary value problem for the ultraslow diffusion equation with the lower-order terms with respect to the spatial variable.

Suggested Citation

  • Vladimir E. Fedorov, 2020. "Generators of Analytic Resolving Families for Distributed Order Equations and Perturbations," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1306-:d:395401
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    Cited by:

    1. 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.

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