Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives

Fedorov, Vladimir E.; Du, Wei-Shih; Kostić, Marko; Abdrakhmanova, Aliya A.

doi:10.3390/math10050681

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Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives

¹

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

²

Laboratory of Functional Materials, South Ural State University, Lenin Av. 76, 454080 Chelyabinsk, Russia

³

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

⁴

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

⁵

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

^*

Author to whom correspondence should be addressed.

Mathematics 2022, 10(5), 681; https://doi.org/10.3390/math10050681

Submission received: 4 February 2022 / Revised: 16 February 2022 / Accepted: 21 February 2022 / Published: 22 February 2022

(This article belongs to the Special Issue Abstract Fractional Integro-Differential Equations and Fixed Point Theory with Applications)

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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.

Keywords: Riemann–Liouville derivative; distributed order equation; analytic resolving family of operators; generator of resolving family; perturbation theorem

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MDPI and ACS Style

Fedorov, V.E.; Du, W.-S.; Kostić, M.; Abdrakhmanova, A.A. Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives. Mathematics 2022, 10, 681. https://doi.org/10.3390/math10050681

AMA Style

Fedorov VE, Du W-S, Kostić M, Abdrakhmanova AA. Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives. Mathematics. 2022; 10(5):681. https://doi.org/10.3390/math10050681

Chicago/Turabian Style

Fedorov, Vladimir E., Wei-Shih Du, Marko Kostić, and Aliya A. Abdrakhmanova. 2022. "Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives" Mathematics 10, no. 5: 681. https://doi.org/10.3390/math10050681

APA Style

Fedorov, V. E., Du, W.-S., Kostić, M., & Abdrakhmanova, A. A. (2022). Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives. Mathematics, 10(5), 681. https://doi.org/10.3390/math10050681

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Analytic Resolving Families for Equations with Distributed Riemann–Liouville Derivatives

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