| 一类高次分数阶微分方程局部解存在性定理 |
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| 引用本文： | 杨慧,郑艳萍.一类高次分数阶微分方程局部解存在性定理[J].成都大学学报(自然科学版),2014,33(3):226-229. |
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| 作者姓名： | 杨慧 郑艳萍 |
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| 作者单位： | 太原师范学院数学系,山西太原,030012 |
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| 基金项目： | 国家自然科学基金，山西省高校科技开发计划，山西省自然科学基金 |
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| 摘 要： | 研究了Riemman-Liouville型导数下的一类高次分数阶微分方程解的存在性问题,所涉及的阶数α为（3,4]的任意实数.给出了所给分数阶微分方程等价的Volterra积分形式,利用泛函分析中的经典方法建立了这类高次分数阶微分方程局部解的存在性定理.
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| 关 键 词： | Riemman-Liouville积分 Riemman-Liouville导数 局部解 |
Existence Theorem of Solutions for One Class of Higher-order Fractional Differential Equations |
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| YANG Hui,ZHENG Yanping.Existence Theorem of Solutions for One Class of Higher-order Fractional Differential Equations[J].Journal of Chengdu University (Natural Science),2014,33(3):226-229. |
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| Authors: | YANG Hui ZHENG Yanping |
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| Institution: | YANG Hui;ZHENG Yanping;Department of Mathematics,Taiyuan Normal University; |
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| Abstract: | This paper studies the existence of solutions of a class of higher order differential equations of fractional order derivative of the Riemman-Liouville type.The order numberα∈（3,4]is any real number.Firstly,we give the Voletrra integral form,which is the equivalent form of differential equations.Secondly,by using the classical method in functional analysis,we establish the existence theorem of local solutions of the higher-order fractional differential equations. |
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| Keywords: | Riemann-Liouville integral Riemann-Liouville differentiation local solution |
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