Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Print: 1064-2315
ISSN Online: 2163-9337

Volume 52, 2020 Volume 51, 2019 Volume 50, 2018 Volume 49, 2017 Volume 48, 2016 Volume 47, 2015 Volume 46, 2014 Volume 45, 2013 Volume 44, 2012 Volume 43, 2011 Volume 42, 2010 Volume 41, 2009 Volume 40, 2008 Volume 39, 2007 Volume 38, 2006 Volume 37, 2005 Volume 36, 2004 Volume 35, 2003 Volume 34, 2002 Volume 33, 2001 Volume 32, 2000 Volume 31, 1999 Volume 30, 1998 Volume 29, 1997 Volume 28, 1996

Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v40.i6.10
pages 1-11

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

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


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.

Articles with similar content:

Differential Games of the Fractional Order with Separated Dynamics
Journal of Automation and Information Sciences, Vol.41, 2009, issue 11
Ivan I. Matychyn, Alexander G. Chentsov, Arkadiy A. Chikriy
On Maximal Initial Data Set in Problems of Practical Stability of Discrete System
Journal of Automation and Information Sciences, Vol.43, 2011, issue 3
Alexander N. Bashnyakov, Ivan V. Khitko , Vladimir V. Pichkur
Peculiarities and Interdependence of Identification and Control Problems under Uncertainty
Journal of Automation and Information Sciences, Vol.42, 2010, issue 2
Alexey V. Gummel, Aleksey O. Zhukov, Vyacheslav F. Gubarev
Pontryagin First Direct Method for Differential Inclusions
Journal of Automation and Information Sciences, Vol.52, 2020, issue 2
Ikromjon M. Iskanadjiev
On Solving and Properties of the Simplest Dynamical Problem of Optimal Set Partition Problem
Journal of Automation and Information Sciences, Vol.45, 2013, issue 6
Elena M. Kiseleva, Larisa S. Koriashkina