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Analysis of existence and structure of solutions for Caputo and Grunwald-Letnikov fractional differential systems

文献类型：期刊论文

作者Peng, E.1; Zhou, Weihong1,3; Xu, Tingting1; Cao, Jie1,2; Liu, Yuxia1; Li, Shangxi1; Zhou, Xueliang1; Zhou, Wei1
刊名AIMS MATHEMATICS
出版日期2025
卷号10期号:12页码:29732-29764
关键词Caputo fractional derivative Grunwald-Letnikov fractional derivative linearly independent solution rank of coefficient matrices
DOI10.3934/math.20251307
文献子类Article
英文摘要In this paper, we investigate the existence and structure of power-type solutions for Caputo fractional differential equation systems (CFDESs) and Grunwald-Letnikov fractional differential equation systems (GLFDESs). Building on the definitions of the Caputo fractional derivative (CFD) and the Grunwald-Letnikov fractional derivative (GLFD), we derive explicit expansion formulas for the fractional differential operators, construct joint coefficient-solution matrices for the considered systems, and, from these, obtain necessary and sufficient rank conditions for the existence of m-th order power solutions. On this basis, we further (1) establish equivalent criteria that guarantee the uniqueness of the degree of power solutions and (2) derive rank-based conditions for the existence of two, and more generally p, linearly independent power particular solutions with distinct degrees. Taken together, these results provide a unified matrix-based theoretical framework for analyzing the existence, uniqueness, and multiplicity of power-type solutions and the associated system structure of the two types of fractional differential systems. Two numerical examples are also provided to demonstrate the validity of the proposed results.
学科主题数学 ; 应用数学
URL标识查看原文
出版地PO BOX 2604, SPRINGFIELD, MO 65801-2604, UNITED STATES
资助项目Yunnan Fundamental Research Projects[202401AU070026]; Yunnan Fundamental Research Projects[202501AT070366]; Scientific Research Foundation Project of Yunnan Education Department[2025Y0720]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:001643709900003
出版者AMER INST MATHEMATICAL SCIENCES-AIMS
资助机构Yunnan Fundamental Research Projects[202401AU070026, 202501AT070366] ; Scientific Research Foundation Project of Yunnan Education Department[2025Y0720]
版本出版稿
源URL[http://ir.ynao.ac.cn/handle/114a53/28803]  
专题云南天文台_中国科学院天体结构与演化重点实验室
通讯作者Zhou, Weihong
作者单位1.School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan, 650504, China;
2.Center for Astrophysics and Great Bay Center of National Astronomical Data Center, Guangzhou University, Guangzhou, 510006, China
3.Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming, Yunnan, 650011, China;
推荐引用方式
GB/T 7714		 Peng, E.,Zhou, Weihong,Xu, Tingting,et al. Analysis of existence and structure of solutions for Caputo and Grunwald-Letnikov fractional differential systems[J]. AIMS MATHEMATICS,2025,10(12):29732-29764.
APA Peng, E..,Zhou, Weihong.,Xu, Tingting.,Cao, Jie.,Liu, Yuxia.,...&Zhou, Wei.(2025).Analysis of existence and structure of solutions for Caputo and Grunwald-Letnikov fractional differential systems.AIMS MATHEMATICS,10(12),29732-29764.
MLA Peng, E.,et al."Analysis of existence and structure of solutions for Caputo and Grunwald-Letnikov fractional differential systems".AIMS MATHEMATICS 10.12(2025):29732-29764.

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