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Journal of Applied MathematicsVolume 2012 2012, Article ID 193061, 21 pages

Research Article

School of Mathematical Science and Computing Technology, Central South University, Hunan, Changsha 410075, China

School of Mathematical Science and Computing Technology, Changsha University of Science and Technology, Hunan, Changsha 410076, China

School of Mathematical Science and Computing Technology, Guangxi University for Nationalities, Guangxi, Nanning 530006, China

Xiamen Institute of Technology, Huaqiao University, Fujian, Xiamen 361021, China

Received 3 March 2012; Revised 21 July 2012; Accepted 23 July 2012

Academic Editor: Chein-Shan Liu

Copyright © 2012 Fang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main purpose of this paper is to obtain the unique solution of the constant coefficient homogeneous linear fractional differential equations 𝐷𝑞𝑡0𝑋𝑡=𝑃𝑋𝑡,𝑋𝑎=𝐵 and the constant coefficient nonhomogeneous linear fractional differential equations 𝐷𝑞𝑡0𝑋𝑡=𝑃𝑋𝑡+𝐷,𝑋𝑎=𝐵 if 𝑃 is a diagonal matrix and 𝑋𝑡∈𝐶1−𝑞𝑡0,𝑇×𝐶1−𝑞𝑡0,𝑇×⋯×𝐶1−𝑞𝑡0,𝑇 and prove the existence and uniqueness of these two kinds of equations for any 𝑃∈𝐿𝑅𝑚 and 𝑋𝑡∈𝐶1−𝑞𝑡0,𝑇×𝐶1−𝑞𝑡0,𝑇×⋯×𝐶1−𝑞𝑡0,𝑇. Then we give two examples to demonstrate the main results.





Autor: Fang Wang, Zhen-hai Liu, and Ping Wang

Fuente: https://www.hindawi.com/



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