Analysis of a System for Linear Fractional Differential Equations

Fang Wang, Zhen-hai Liu and Ping Wang

Journal of Applied Mathematics, 2012, vol. 2012, 1-21

Abstract:

The main purpose of this paper is to obtain the unique solution of the constant coefficient homogeneous linear fractional differential equations ð · ð ‘ž ð ‘¡ 0 ð ‘‹ ( ð ‘¡ ) = 𠑃 ð ‘‹ ( ð ‘¡ ) , ð ‘‹ ( ð ‘Ž ) = ð µ and the constant coefficient nonhomogeneous linear fractional differential equations ð · ð ‘ž ð ‘¡ 0 ð ‘‹ ( ð ‘¡ ) = 𠑃 ð ‘‹ ( ð ‘¡ ) + ð · , ð ‘‹ ( ð ‘Ž ) = ð µ if 𠑃 is a diagonal matrix and ð ‘‹ ( ð ‘¡ ) ∈ ð ¶ 1 − ð ‘ž [ ð ‘¡ 0 , 𠑇 ] × ð ¶ 1 − ð ‘ž [ ð ‘¡ 0 , 𠑇 ] × ⋯ × ð ¶ 1 − ð ‘ž [ ð ‘¡ 0 , 𠑇 ] and prove the existence and uniqueness of these two kinds of equations for any 𠑃 ∈ ð ¿ ( ð ‘… ð ‘š ) and ð ‘‹ ( ð ‘¡ ) ∈ ð ¶ 1 − ð ‘ž [ ð ‘¡ 0 , 𠑇 ] × ð ¶ 1 − ð ‘ž [ ð ‘¡ 0 , 𠑇 ] × ⋯ × ð ¶ 1 − ð ‘ž [ ð ‘¡ 0 , 𠑇 ] . Then we give two examples to demonstrate the main results.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:193061

DOI: 10.1155/2012/193061

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