| 摘要: |
| 分数阶微积分被广泛应用于流体力学、电化学分析、生物系统的电传导等领域，分数阶微分方程的边值问题已成为研究热点，无限区间上的边值问题是其中比较困难的部分，针对这种边值问题，提出了一类无穷区间上具有积分边界条件的分数阶耦合微分方程；应用格林函数及分数阶微积分的有关结论，将这类无穷区间上具积分边界条件的分数阶耦合微分方程边值问题转化为等价的积分系统；引入函数乘积空间和二维积分算子，借助锥上Krasnoselskii不动点定理，并利用一些分析技巧，得到此边值问题至少存在一个正解的充分条件，建立了无限区间上分数阶耦合边值问题正解存在性的新结果。 |
| 关键词: 无穷区间 分数阶耦合微分系统 锥上不动点定理 积分边界条件 |
| DOI： |
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| Existence of Positive Solutions for Integral Boundary Problem of Coupled Fractional Differential Systems on Infinite Interval |
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XU Wen-xu，ZHOU Zong-fu
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| Abstract: |
| Fractional calculus is widely used in fluid mechanics，electrochemical analysis，the electric conduction of biological systems and other fields. Boundary value problems of fractional differential equations has become a popular research and the problem in infinite interval is a difficult part. Aiming at these boundary value problems，this paper proposes a class of integral boundary problems of coupled fractional differential systems on infinite interval. By applying the properties of Green and conclusion of fractional calculus，the integral boundary problem of coupled fractional differential systems on infinite interval is transformed into equivalent integral system. By leading into product spaces，two-dimensional integral operators and using Krasnoselskii fixed point theorem on cone，some analytical skills，the sufficient condition of existence of at least one positive solution for the boundary value problem and new results of existence of positive solutions for integral boundary problem of coupled fractional differential systems on infinite interval are obtained. |
| Key words: infinite interval coupled fractional differential systems fixed point theorem on cone integral boundary condition |
