| 分数阶时滞广义Logistic方程解的研究 |
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| 引用本文： | 袁利国.分数阶时滞广义Logistic方程解的研究[J].中山大学学报(自然科学版),2014,53(2):44-48. |
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| 作者姓名： | 袁利国 |
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| 作者单位： | 0529-6579(2014)02-0044-05 |
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| 基金项目： | 国家自然科学基金资助项目(11271139);广东省自然科学基金资助项目(S2013040016144) |
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| 摘 要： | 基于Banach不动点定理与分数阶微积分的相关性质,首先研究了分数阶时滞广义Logistic方程解的存在唯一性,同时得到解的一致稳定性的充分条件。最后,利用改进的Adams-Bashforth-Moulton预估-校正算法得到其数值解。
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| 关 键 词： | Caputo分数阶导数 分数阶时滞Logistic方程 Banach不动点定理 存在唯一性 |
| 收稿时间： | 2013-08-23; |
Research on Solutions of Fractional-Order Generalized Logistic Equation with Delay |
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| YUAN Liguo.Research on Solutions of Fractional-Order Generalized Logistic Equation with Delay[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2014,53(2):44-48. |
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| Authors: | YUAN Liguo |
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| Institution: | Department of Mathematics, South China Agricultural University, Guangzhou 510642, China |
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| Abstract: | Based on the Banach fixed point theorem and properties of differential and integral calculus of fractional order, the existence and uniqueness of solutions for the fractional-order generalized Logistic equation with delay are discussed. Some sufficient conditions for uniform stability of solutions are obtained. The numerical solution is obtained by the modified Adams-Bashforth-Moulton predictor-corrector scheme. |
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| Keywords: | fractional-order derivative of Caputo fractional-order logistic equation with delay Banach's fixed point theorem existence and uniqueness |
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