On definition of solution of initial value problem for fractional differential equation of variable order

被引：3

作者：

Zhang, Shuqin ^{[1
]}

Wang, Jie ^{[1
]}

Hu, Lei ^{[2
]}

机构：

[1] China Univ Min & Technol Beijing, Dept Math, Beijing 100083, Peoples R China

[2] Shandong Jiaotong Univ, Sch Sci, Jinan 250357, Peoples R China

来源：

AIMS MATHEMATICS | 2021年 / 6卷 / 07期

基金：

中国国家自然科学基金;

关键词：

variable order Caputo fractional derivative; variable order fractional integral; fractional differential equations; initial value problem; approximate solution; BOUNDARY-VALUE-PROBLEMS; NUMERICAL TECHNIQUE; EXISTENCE; DERIVATIVES;

D O I：

10.3934/math.2021401

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a new definition of continuous approximate solution to initial value problem for differential equations involving variable order Caputo fractional derivative based on the classical definition of solution of integer order (or constant fractional order) differential equation. Some examples are presented to illustrate these theoretical results.

引用

页码：6845 / 6867

页数：23

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