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非线性隐式分数阶微分方程耦合系统初值问题

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非线性隐式分数阶微分方程耦合系统初值问题 董佳华1, 冯育强2, 蒋君11. 武汉科技大学理学院, 武汉 430065;
2. 冶金工业过程系统科学湖北省重点实验室, 武汉 430081 The Proximal Point Iterative Algorithm for the Initial Value Problem for a Coupled System of Nonlinear Implicit for Fractional Differential Equations Dong Jiahua1, Feng yuqiang2, Jiang Jun11. School of Science, Wuhan University of Science and Technology, Wuhan 430065, China;
2. Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, China
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摘要利用不动点定理和向量形式的Gronwall不等式,得到了Caputo分数阶导数定义下的非线性隐式分数阶微分方程耦合系统解的存在性和唯一性,并探讨了解的估值,解对初值的连续依赖性,解对参数和函数的连续依赖性,以及耦合系统的ε-近似解.
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收稿日期: 2018-01-18
PACS:O175
基金资助:国家自然科学基金(61473338)及教育部高等学校博士点基金(20134219120003)资助项目.

引用本文:
董佳华, 冯育强, 蒋君. 非线性隐式分数阶微分方程耦合系统初值问题[J]. 应用数学学报, 2019, 42(3): 356-370. Dong Jiahua, Feng yuqiang, Jiang Jun. The Proximal Point Iterative Algorithm for the Initial Value Problem for a Coupled System of Nonlinear Implicit for Fractional Differential Equations. Acta Mathematicae Applicatae Sinica, 2019, 42(3): 356-370.
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http://123.57.41.99/jweb_yysxxb/CN/ http://123.57.41.99/jweb_yysxxb/CN/Y2019/V42/I3/356


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