A Class of Fractional Degenerate Evolution Equations with Delay

Mathematics

卷:8

VladimirE. Fedorov¹  Amar Debbouche² 

[1] Department of Mathematical Analysis, Chelyabinsk State University, 129 Kashirin Brothers St., Chelyabinsk 454001, Russia;

[2] Department of Mathematics, Guelma University, Guelma 24000, Algeria;

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

DOI  :  10.3390/math8101700

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown