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| 分数阶时滞微分方程正解的存在性 | |
| 引用本文： | 廖春平,叶海平. 分数阶时滞微分方程正解的存在性[J]. 纺织高校基础科学学报, 2008, 21(4): 415-420 |
| 作者姓名： | 廖春平 叶海平 |
| 作者单位： | 东华大学,应用数学系,上海,201620 |
| 摘 要： | 研究了一类非线性分数阶时滞微分方程{L（D）[x（t）-x（0）3-f（t，xl），0〈t≤T，x（t）=9（t）≥0，t∈[-r，0]正解的存在性和惟一性．在f（t，·）非减的条件下，通过运用上下解的方法，获得了该方程正解存在的充分条件，并利用Banach不动点定理证明了该方程正解的惟一性． |
| 关 键 词： | Riemann—Liouville分数阶导数 时滞 分数阶微分方程 正解 |
Existence of positive solutions of nonlinear fractional differential equations with delay |
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| LIAO Chun-ping,YE Hai-ping. Existence of positive solutions of nonlinear fractional differential equations with delay[J]. Basic Sciences Journal of Textile Universities, 2008, 21(4): 415-420 | |
| Authors: | LIAO Chun-ping YE Hai-ping |
| Affiliation: | LIAO Chun-ping , YE Hai-ping (Department of Applied Mathematics, Donghua University, Shanghai 201620,China) |
| Abstract: | The existence and uniqueness of positive solutions for a class of nonlinear fractional differential equation with delay {L（D）[x（t）-x（0）3-f（t,xl）,0〈t≤T, x（t）=9（t）≥0,t∈[-r,0] is investigated. By using the sub and super-solution method, some suffcient conditions for its existence of positive solutions are obtained under the condition that f（t, ~ ） is nondecreasing, and the uniqueness of a positive solution is showed by application of the Banach fixed point theorem. |
| Keywords: | Riemann-Liouville fractional derivative delay fractional differential equation positive solution |
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