一类非线性分数阶多点边值问题的可解性

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 655-668.

一类非线性分数阶多点边值问题的可解性

郝晓红|程智龙*|周宗福

安徽工程大学机电学院基础教学部安徽芜湖 |241000；安徽大学数学科学学院合肥 |230601

收稿日期:2012-10-17 修回日期:2013-12-29 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
国家自然科学基金(11071001)和安徽省自然科学基金(1208085MA13)资助

Solvability of Solutions for a Class of Nonlinear Fractional Multi-Point Boundary Value Problems

HAO Xiao-Hong, CHENG Zhi-Long*|ZHOU Zong-Fu

Basic Teaching Department, College of Mechanical &|Electrical |Engineering, Anhui Polytechnic University, Anhui Wuhu 241000；School of Mathematical Sciences, |Anhui University, Hefei 230601

Received:2012-10-17 Revised:2013-12-29 Online:2014-06-25 Published:2014-06-25
Supported by:
国家自然科学基金(11071001)和安徽省自然科学基金(1208085MA13)资助

摘要/Abstract

摘要：

研究下面一类非线性分数阶微分方程多点边值问题
D^α₀₊u(t) = f(t, u(t), D^α-1₀₊u(t), D^α-2₀₊u(t), D^α-3₀₊u(t)), t ∈(0,1), 3<α≤4, u(0) = 0, D^α^-1₀₊u(0)=∑^m_i₌₁α_iD^α-1₀₊u(ξ_i),
D^α-2₀₊u(1)=∑_j=1ⁿβ_jD^α-2₀₊u(η_j), D^α-3₀₊u(1)-D^α-3₀₊u(0)=D^α^-2₀₊u(1) 1/2D^α-1₀₊u(0).
通过应用Mawhin重合度理论得到解的存在性结果. 此结论拓展了在分数阶多点边值问题这个领域的以前的结果.

关键词: 分数阶微分方程, 边值问题, 重合度理论, 可解性

Abstract:

This paper is concerned with the following nonlinear fractional differential equations multi-point boundary value problem
D^α₀₊u(t) = f(t, u(t), D^α-1₀₊u(t), D^α-2₀₊u(t), D^α-3₀₊u(t)), t ∈(0,1),

u(0) = 0, D^α^-1₀₊u(0)=∑^m_i₌₁α_iD^α-1₀₊u(ξ_i),
D^α-2₀₊u(1)=∑_j=1ⁿβ_jD^α-2₀₊u(η_j), D^α-3₀₊u(1)-D^α-3₀₊u(0)=D^α^-2₀₊u(1) 1/2D^α-1₀₊u(0).
By applying Mawhin coincidence degree theory, we obtain the existence of the solutions for the problem. The results expand the previous ones in the field.

Key words: Fractional differential equation, Boundary value problem, Coincidence degree theory, Solvability of the solutions

中图分类号:

34B10

郝晓红, 程智龙, 周宗福. 一类非线性分数阶多点边值问题的可解性[J]. 数学物理学报, 2014, 34(3): 655-668.

HAO Xiao-Hong, CHENG Zhi-Long, ZHOU Zong-Fu. Solvability of Solutions for a Class of Nonlinear Fractional Multi-Point Boundary Value Problems[J]. Acta mathematica scientia,Series A, 2014, 34(3): 655-668.

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