General history-dependent operators with applications to differential equations

Miskolc Mathematical Notes

article

Xiuwen Li¹  Biao Zeng¹ 

[1] Guangxi University for Nationalities, Faculty of Mathematics and Physics

关键词: general history-dependent operator;    fixed point theorem;    differential equation;    fractional derivative.;   

DOI  :  10.18514/MMN.2022.2913

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

In this paper, we introduce a class of nonlinear operators--the class of general history-dependent operators. These are the operators defined on spaces of functions endowed with a structure of Banach space (the case of bounded interval of time) or Fr\'{e}chet space (the case of unbounded interval of time). We state and prove various properties of such operators, including fixed point properties. Moreover, we also study several classes of differential equations in Banach spaces, for which we our previous results can be applied.

【 授权许可】

CC BY