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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (4): 599-607.doi: 10.3969/j.issn.1005-3085.2015.04.013

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分数阶描述系统的可解性和正性(英)

丁小丽   

  1. 西安工程大学数学系，西安 710048
  • 收稿日期:2014-03-25 接受日期:2014-10-27 出版日期:2015-08-15 发布日期:2015-10-15
  • 基金资助:
    陕西省科技规划项目 (2014JQ1041)；陕西省教育厅科研项目 (14JK1300)；西安工程大学博士点科研业务费专项基金 (BS1342).

Solvability and Positivity of Fractional Descriptor Systems

DING Xiao-li   

  1. Department of Mathematics, Xi'an Polytechnic University, Xi'an 710048
  • Received:2014-03-25 Accepted:2014-10-27 Online:2015-08-15 Published:2015-10-15
  • Supported by:
    The Science and Technology Planning Project of Shaanxi Province (2014JQ1041); the Scientific Research Program Funded by Shaanxi Provincial Education Department (14JK1300); the Research Fund for the Doctoral Program of Xi'an Polytechnic University (BS1342).

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摘要： 分数阶描述系统是一类重要的分数阶微分系统，在含有超导材料的集成电路模拟等工程物理问题中具有广泛的应用．本文主要研究了一类型分数阶描述系统的可解性，得到了该类系统的解析解，并建立了该类系统正性的充分条件．通过一个例子展示了所得结果的可行性和实用性．利用本文中的方法，可以得到含有不同阶的分数阶描述系统的可解性、解析解以及正性的充分条件．

关键词: 分数阶描述系统, 可解性, 正性

Abstract:

Fractional descriptor systems belong to an important class of fractional differential systems. The systems have a wide range of applications in physical and engineering problems such as integrated circuits with superconductor materials. In this paper, a new class of fractional descriptor systems is considered and solvability of the fractional descriptor systems is discussed. Furthermore, explicit solutions of the fractional descriptor systems are given and sufficient conditions for the positivity of the fractional descriptor systems are established. An example is presented to illustrate the feasibility and applications of the obtained results. Our results can be extended to the case of fractional descriptor systems with different fractional orders.

Key words: fractional descriptor systems, solvability, positivity

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