General fractional interval-valued differential equations and Gronwall inequalities

被引：2

作者：

Fan, Qin ^{[1
,2
]}

Huang, Lan-Lan ^{[2
]}

Wu, Guo-Cheng ^{[2
]}

机构：

[1] Chongqing Univ Posts & Telecommun, Sch Sci, Chongqing 400065, Peoples R China

[2] Neijiang Normal Univ, Coll Math & Informat Sci, Data Recovery Key Lab Sichuan Prov, Neijiang 641100, Peoples R China

来源：

SOFT COMPUTING | 2023年 / 27卷 / 12期

基金：

中国国家自然科学基金;

关键词：

General fractional calculus; Interval-valued function; Gronwall inequality; Interval-valued analysis; CALCULUS; EXISTENCE;

D O I：

10.1007/s00500-023-08046-7

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Interval-valued systems with the general fractional derivative are defined on closed intervals on the real line R. Function spaces of the fractional integrals and derivatives are discussed. Then some fundamental theorems of the Caputo and Riemann-Liouville derivatives are provided, respectively. Finally, the interval-valued Gronwall inequalities are presented as one application.

引用

页码：7739 / 7749

页数：11

共 50 条

[1] General fractional interval-valued differential equations and Gronwall inequalities
Qin Fan
Lan-Lan Huang
Guo-Cheng Wu
Soft Computing, 2023, 27 : 7739 - 7749
[2] On Gronwall type inequalities for interval-valued functions on time scales
Awais Younus
Muhammad Asif
Khurram Farhad
Journal of Inequalities and Applications, 2015
[3] On Gronwall type inequalities for interval-valued functions on time scales
Younus, Awais
Asif, Muhammad
Farhad, Khurram
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015,
[4] Numerical solutions of interval-valued fractional nonlinear differential equations
Lan-Lan Huang
Bao-Qing Liu
Dumitru Baleanu
Guo-Cheng Wu
The European Physical Journal Plus, 134
[5] Numerical solutions of interval-valued fractional nonlinear differential equations
Huang, Lan-Lan
Liu, Bao-Qing
Baleanu, Dumitru
Wu, Guo-Cheng
EUROPEAN PHYSICAL JOURNAL PLUS, 2019, 134 (05):
[6] Interval-valued fuzzy derivatives and solution to interval-valued fuzzy differential equations
Kalani, Hadi
Akbarzadeh-T, Mohammad-R.
Akbarzadeh, Alireza
Kardan, Iman
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2016, 30 (06) : 3373 - 3384
[7] Some new variants of interval-valued Gronwall type inequalities on time scales
Younus, A.
Asif, M.
Farhad, K.
Nisar, O.
IRANIAN JOURNAL OF FUZZY SYSTEMS, 2019, 16 (05): : 187 - 198
[8] Generalized Gronwall inequalities and their applications to fractional differential equations
Lin, Shi-you
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
[9] Generalized Gronwall inequalities and their applications to fractional differential equations
Shi-you Lin
Journal of Inequalities and Applications, 2013
[10] The numerical solution for the interval-valued differential equations
Pan, Li-Xia
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2015, 19 (04) : 632 - 641

← 1 2 3 4 5 →