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Volume 8
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Article

A Class of Fractional Degenerate Evolution Equations with Delay

by
Amar Debbouche
1,* and
Vladimir E. Fedorov
2,3,4
1
Department of Mathematics, Guelma University, Guelma 24000, Algeria
2
Department of Mathematical Analysis, Chelyabinsk State University, 129 Kashirin Brothers St., Chelyabinsk 454001, Russia
3
Laboratory of Functional Materials, South Ural State University (National Research University), Lenin Av. 76, Chelyabinsk 454080, Russia
4
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
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(10), 1700; https://doi.org/10.3390/math8101700
Submission received: 31 August 2020 / Revised: 21 September 2020 / Accepted: 28 September 2020 / Published: 3 October 2020
(This article belongs to the Special Issue Models of Delay Differential Equations)
Versions Notes

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.
Keywords: Gerasimov–Caputo fractional derivative; differential equation with delay; degenerate evolution equation; fixed point theorem Gerasimov–Caputo fractional derivative; differential equation with delay; degenerate evolution equation; fixed point theorem

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MDPI and ACS Style

Debbouche, A.; Fedorov, V.E. A Class of Fractional Degenerate Evolution Equations with Delay. Mathematics 2020, 8, 1700. https://doi.org/10.3390/math8101700

AMA Style

Debbouche A, Fedorov VE. A Class of Fractional Degenerate Evolution Equations with Delay. Mathematics. 2020; 8(10):1700. https://doi.org/10.3390/math8101700

Chicago/Turabian Style

Debbouche, Amar, and Vladimir E. Fedorov. 2020. "A Class of Fractional Degenerate Evolution Equations with Delay" Mathematics 8, no. 10: 1700. https://doi.org/10.3390/math8101700

APA Style

Debbouche, A., & Fedorov, V. E. (2020). A Class of Fractional Degenerate Evolution Equations with Delay. Mathematics, 8(10), 1700. https://doi.org/10.3390/math8101700

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