A Class of Fractional Degenerate Evolution Equations with Delay

Amar Debbouche and Vladimir E. Fedorov
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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

Mathematics, 2020, vol. 8, issue 10, 1-8

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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