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Journal of Automation and Information Sciences

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Presentation of Solutions of Linear Systems with Fractional Derivatives in the Sense of Riemann-Liouville, Caputo and Miller-Ross

Volume 40, Edição 6, 2008, pp. 1-11
DOI: 10.1615/JAutomatInfScien.v40.i6.10
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Arkadiy A. Chikriy
V.M. Glushkov Institute of Cybernetics National Academy of Sciences of Ukraine 40 Akadem. Glushkov Ave., Kiev, 03187, Ukraine
Ivan I. Matichin
V. M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kyiv, Ukraine

RESUMO

Consideration is given to inhomogeneous linear systems of differential equations with classical Riemann-Liouville fractional derivatives as well as the regularized Caputo derivative and sequential Miller-Ross fractional derivatives. Using Laplace transform the solutions of such systems are presented in terms of matrix Mittag-Leffler functions as analogues of Cauchy formula for arbitrary Lebesque measurable and bounded functions of time in the right-hand side. These relations play a key role in solving related problems of mathematical control theory and theory of dynamic games.

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