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On systems of linear fractional differential equations with constant coefficients. (English) Zbl 1121.34006

Summary: This paper deals with the study of linear systems of fractional differential equations such as the following system:

Y ¯ (α =𝐀(x)Y ¯+𝐁 ¯(x),(1)

where Y ¯ (α is the Riemann-Liouville or the Caputo fractional derivative of order α(0<α1), and

𝐀(x)=a 11 (x)a 1n (x)···a n1 (x)a nn (x);𝐁 ¯(x)=b 1 (x)b n (x)

are matrices of known real functions. In a way analogous to the usual case, we show how a generalized matrix exponential function and certain fractional Green function, in connection with the Mittag-Leffler type functions, would allow us to obtain an explicit representation of the general solution to the system (1) when 𝐀 is a constant matrix.

MSC:
34A30Linear ODE and systems, general