| 带有积分边值条件的分数阶微分包含解的存在性 |
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| 引用本文： | 李建利,陈丽珍,李刚.带有积分边值条件的分数阶微分包含解的存在性[J].数学进展,2020(2):185-194. |
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| 作者姓名： | 李建利 陈丽珍 李刚 |
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| 作者单位： | 太原学院应用数学系;山西财经大学应用数学学院;扬州大学数学科学学院 |
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| 基金项目： | 国家自然科学基金(No.11871064)。 |
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| 摘 要： | 本文利用Hausdorff非紧测度、分数阶的微积分理论和Kakutani不动点定理,研究了满足条件z(0)=z0,z(1)=λcI0+γ+z(η)=λ∫0η(η-s)γ-1/Γ(γ)z(s)ds的广义Bagley-Torvik型分数阶微分包含cDv1 z(t)-ac Dv2 Z(t)∈F(t,z(t)),t∈(0,1)解的存在性.其中1 0,a和λ是给定的常数.
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| 关 键 词： | HAUSDORFF非紧测度 分数阶微分包含 KAKUTANI不动点定理 |
The Existence of Solutions of Fractional Differential Inclusions with Integral Boundary Value Conditions |
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| LIJianli,CHEN Lizhen,LI Gang.The Existence of Solutions of Fractional Differential Inclusions with Integral Boundary Value Conditions[J].Advances in Mathematics,2020(2):185-194. |
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| Authors: | LIJianli CHEN Lizhen LI Gang |
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| Institution: | (Department of Applied Mathematics,Taiyuan Institute,Taiyuan,Shanxi,030032,P.R.China;School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan,Shanxi,030006,P.R.China;School of Mathematical Sciences,Yangzhou University,Yangzhou,Jiangsu,225002,P.R.China) |
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| Abstract: | We consider the generalized Bagley-Torvik type fractional differential inclusion cDv1(t)-ac Dv2 Z(t)∈F(t,z(t)),t∈(0,1)meet to z(0)=z0,z(1)=λcI0+γ+z(η)=λ∫0η(η-s)γ-1/Γ(γ)z(s)ds,where 1 0,a and λ are given constants in this article.By the noncompactness measure of Hausdorff,fractional calculus theory and Kakutani fixed point theorem,we prove the existence of solutions.Our result extends the existence theorems for the Bagley-Torvik type equation. |
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| Keywords: | noncompactness measure of Hausdorff fractional differential inclusions Kakutani fixed point theorem |
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