Fundamental results to the weighted Caputo-type differential operator

被引：20
作者：
Liu, Jian-Gen [1 ,2 ]
Yang, Xiao-Jun [1 ,2 ,3 ]
Feng, Yi-Ying [2 ,3 ]
Geng, Lu-Lu [1 ,2 ]
机构：
[1] China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China
[2] China Univ Min & Technol, State Key Lab Geomech & Deep Underground Engn, Xuzhou 221116, Jiangsu, Peoples R China
[3] China Univ Min & Technol, Sch Mech & Civil Engn, Xuzhou 221116, Jiangsu, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2021年 / 121卷
关键词：
Weighted Caputo-type integral; Weighted Caputo-type differential operator; Differential equation; EQUATION;
D O I：
10.1016/j.aml.2021.107421
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this letter, we defined a weighted Caputo-type differential operator which was used to character relaxation and diffusion models in two different types. Then, one of the weighted Caputo-type integral operators by solving the related linear differential equation was also defined. Subsequently, we studied their main properties. Lastly, the existence of a unique solution of the related nonlinear differential equation through the Banach fixed point theorem was presented. These basic facts lay a solid foundation for the concrete practice in the future. (C) 2021 Elsevier Ltd. All rights reserved.
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页数：7
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