逐次逼近法在分数阶 $q$-微分方程初值问题中的应用

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 1900-1931.

逐次逼近法在分数阶 $q$-微分方程初值问题中的应用

郭彩霞^*(), 郭建敏(), 康淑瑰(), 李华鹏()

山西大同大学数学与统计学院, 山西大同 037009

收稿日期:2025-08-11 修回日期:2026-04-27 出版日期:2026-10-26 发布日期:2026-09-07
通讯作者: 郭彩霞 E-mail:iris-gcx@163.com;dtdxguojianmin@163.com;dtkangshugui@126.com;lihuaa1_0@163.com
作者简介:郭建敏, E-mail:dtdxguojianmin@163.com;
康淑瑰, E-mail:dtkangshugui@126.com;
李华鹏, E-mail:lihuaa1_0@163.com
基金资助:
国家自然科学基金(11871314);山西省自然科学基金(202303021221168);装备保障算法创新团队项目

The Successive Approximation Method for the Initial Value Problem of $q$-fractional Differential Equations

Caixia Guo^*(), Jianmin Guo(), Shugui Kang(), Huapeng Li()

School of Mathematics and Statistics, Shanxi Datong University, Shanxi Datong 037009

Received:2025-08-11 Revised:2026-04-27 Online:2026-10-26 Published:2026-09-07
Contact: Caixia Guo E-mail:iris-gcx@163.com;dtdxguojianmin@163.com;dtkangshugui@126.com;lihuaa1_0@163.com
Supported by:
NSFC(11871314);Shanxi Provincial Natural Science Foundation(202303021221168);Equipment Support Algorithm Innovation Team Project

摘要/Abstract

摘要：

该文采用逐次逼近法讨论了一类分数阶 $q$-微分方程初值问题解的存在性及其系统解的存在性, 然后给出了两类特殊分数阶 $q$-微分方程初值问题 (分数阶 $q$-微分受电弓方程和分数阶 $q$- 微分 Ambartsumian 方程) 及相应系统的近似解. 并着重讨论和分析了两类特殊方程近似解的几个性质.

关键词: 初值问题, 分数阶 $q$-微分, 逐次逼近法, 近似解

Abstract:

This paper employs the method of successive approximations to investigate the existence of solutions for a class of initial value problems of fractional $q$-difference equations, as well as the existence of solutions for their corresponding systems. Subsequently, it presents approximate solutions for two specific types of fractional $q$-difference initial value problems (the fractional $q$-difference pantograph equation and the fractional $q$-difference Ambartsumian equation) along with their associated systems. Special emphasis is placed on discussing and analyzing several key properties of the approximate solutions for these two special equations.

Key words: initial value problem, fractional $q$-differential, continuous approximation method, approximate solutions

中图分类号:

O175.1

郭彩霞, 郭建敏, 康淑瑰, 李华鹏. 逐次逼近法在分数阶 $q$-微分方程初值问题中的应用[J]. 数学物理学报, 2026, 46(5): 1900-1931.

Caixia Guo, Jianmin Guo, Shugui Kang, Huapeng Li. The Successive Approximation Method for the Initial Value Problem of $q$-fractional Differential Equations[J]. Acta mathematica scientia,Series A, 2026, 46(5): 1900-1931.

图/表 2

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