抽象多项Riemann-Liouville分数阶微分方程

数学物理学报 ›› 2016, Vol. 36 ›› Issue (4): 601-622.

• 论文 • 下一篇

抽象多项Riemann-Liouville分数阶微分方程

Marko Kosti?¹, 李成刚², 李淼³

1. University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovica 6, 21125 Novi Sad, Serbia;
2. 西南交通大学峨眉校区基础课部四川峨眉山 614202;
3. 四川大学数学学院成都 610065

收稿日期:2015-09-21 修回日期:2016-05-13 出版日期:2016-08-26 发布日期:2016-08-26
通讯作者: 李淼 E-mail:limiao1973@hotmail.com
作者简介:Marko Kostić,marco.s@verat.net;李成刚,lichenggang@home.swjtu.edu.cn
基金资助:
174024 of Ministry of Science and Technological Development，Republic of Serbia、国家自然科学基金（11371263）和教育部新世纪优秀人才基金资助

Abstract Multi-Term Fractional Differential Equations with Riemann-Liouville Derivatives

Marko Kosti?¹, Li Chenggang², Li Miao³

1. University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovi?a 6, 21125 Novi Sad, Serbia;
2. Department of Foundational Courses, Southwest Jiaotong University-Emei, Sichuan Emeishan 614202;
3. Department of Mathematics, Sichuan University, Chengdu 610065

Received:2015-09-21 Revised:2016-05-13 Online:2016-08-26 Published:2016-08-26
Supported by:
Supported by the 174024 of Ministry of Science and Technological Development,Republic of Serbia,the NSFC(11371263) and the Program for New Century Excellent Talents in University of China

摘要/Abstract

摘要：

该文研究如下抽象多项分数阶微分方程
D_t^αnu（t）+A_jD_t^αju（t）=AD_t^αu（t）+f（t），t∈（0，τ），（0.1）
其中n∈N\{1}，算子A，A₁，…，A_n-1为复Banach空间E上的闭线性算子，0≤α₁<…<α_n，0≤α<α_n，0<τ≤∞，f（t）为E-值函数，D_t^α表示α阶Riemann-Liouville分数阶导数^[5]. 延续着作者先前在文献[22，24-25]和[34]中的研究工作，该文引入并系统分析方程（0.1）的若干类新的k-正则（C₁，C₂）-存在和唯一（生成）族，并对抽象的理论性结果给出了丰富的例子来阐明.

关键词: 抽象多项分数阶微分方程, Riemann-Liouville分数阶导数, (a, k)-正则C-豫解族, 适定性

Abstract:

In this paper, we investigate the following abstract multi-term fractional differential equation
D_t^αnu（t）+A_jD_t^αju(t)=AD_t^αu(t)+f(t),t∈(0,τ),
where n∈N\{1}, A and A₁,…,A_n-1 are closed linear operators on a complex Banach space E, 0≤α₁<…<α_n, 0≤α<α_n, 0<τ≤∞, f(t) is an E-valued function, and D_t^α denotes the Riemann-Liouville fractional derivative of order α ([5]). We introduce and systematically analyze several new types of k-regularized (C₁,C₂)-existence and uniqueness (propagation) families for (0.1), continuing in such a way our previous researches raised in [22, 24-25] and [34]. Plenty of various examples illustrates our abstract results.

Key words: Abstract multi-term fractional differential equations, Riemann-Liouville fractional derivatives, (a,k)-Regularized C-resolvent families, Well-posedness

中图分类号:

O175.2

Marko Kostić, 李成刚, 李淼. 抽象多项Riemann-Liouville分数阶微分方程[J]. 数学物理学报, 2016, 36(4): 601-622.

Marko Kostić, Li Chenggang, Li Miao. Abstract Multi-Term Fractional Differential Equations with Riemann-Liouville Derivatives[J]. Acta mathematica scientia,Series A, 2016, 36(4): 601-622.

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抽象多项Riemann-Liouville分数阶微分方程

Abstract Multi-Term Fractional Differential Equations with Riemann-Liouville Derivatives

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