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The constant variation formulae for singular fractional differential systems with delay. (English) Zbl 1189.34153
Summary: This paper considers the Caputo singular fractional differential systems with delay, and the Riemann-Liouville singular fractional differential systems with delay. A new function α-δ is defined. By the D - inverse matrix and α-δ function, two fundamental solutions are given. The constant variation formulae for singular fractional differential systems with delay are obtained.
MSC:
34K37Functional-differential equations with fractional derivatives
26A33Fractional derivatives and integrals (real functions)
45J05Integro-ordinary differential equations
References:
[1]Das, Shantanu: Functional fractional calculus for system identification and controls, (2008)
[2]Podlubny, I.: Fractional differential equations, (1999)
[3]Miller, K. S.; Boss, B.: An introduction to the fractional calculus and fractional differential equations, (1993)
[4]Lakshmikantham, V.: Theory of fractional functional differential equations, Nonlinear analysis 69, No. 10, 3337-3343 (2008) · Zbl 1162.34344 · doi:10.1016/j.na.2007.09.025
[5]Zhou, Yong: Existence and uniqueness of fractional functional differential equations with unbounded delay, International journal of dynamical systems and differential equations 4, No. 1, 239-244 (2008) · Zbl 1175.34081 · doi:10.1504/IJDSDE.2008.022988
[6]Bonilla, B.; Rivero, M.; Trujillo, J. J.: On systems of linear fractional differential equations with constant coefficients, Applied mathematics and computation 187, No. 1, 68-78 (2007) · Zbl 1121.34006 · doi:10.1016/j.amc.2006.08.104
[7]Arikoglu, Aytac; Ozkol, Ibrahim: Solution of fractional differential equations by using differential transform method, Chaos, solitons, fractals 34, No. 5, 1473-1481 (2007) · Zbl 1152.34306 · doi:10.1016/j.chaos.2006.09.004
[8]Ibrahim, Rabha W.; Momani, Shaher: On the existence and uniqueness of solutions of a class of fractional differential equations, Journal of mathematical analysis and applications 334, No. 1, 1-10 (2007) · Zbl 1123.34302 · doi:10.1016/j.jmaa.2006.12.036
[9]Araya, Daniela; Lizama, Carlos: Almost automorphic mild solutions to fractional differential equations, Nonlinear analysis 69, No. 11, 3692-3705 (2008) · Zbl 1166.34033 · doi:10.1016/j.na.2007.10.004
[10]Hale, Jack K.; Lunel, Sjoerd M. Verduyn: Introduction to functional differential equations, (1992)
[11]Wei, Jiang: The degenerate differential systems with delay, (1998)
[12]Thomas Erneux, Applied Delay Differential Equations, Acta Mathematica Scientia, Springer Science-Business Media, LLC, 2009
[13]Wei, Jiang: Eigenvalue and stability of singular differential delay systems, Journal of mathematical analysis and applications 297, 305-316 (2004) · Zbl 1063.34052 · doi:10.1016/j.jmaa.2004.05.008
[14]Wei, Jiang; Song, Wenzhong: Controllability of singular systems with control delay, Automatica 37, 1873-1877 (2001) · Zbl 1058.93012 · doi:10.1016/S0005-1098(01)00135-2
[15]Byers, Ralph; Kunkel, Peter; Mehrmann, Volker: Regularization of linear descriptor systems with variable coefficients, SIAM journal on control and optimization 35, No. 1, 117-133 (1997) · Zbl 0895.93026 · doi:10.1137/S0363012994278936
[16]Dai, L.: Singular control systems, (1989)
[17]Campbell, S. L.: Singular systems of differential equation (II), (1982)