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Laplace transform and fractional differential equations. (English) Zbl 1238.34013

The authors establish a sufficient condition for solving the constant coefficient matrix fractional differential equation by using Laplace transform. Further, the authors provide a solution representation for the matrix fractional differential equation using the Mittag-Leffler function.

MSC:

34A08 Fractional ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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[1] Podlubny, I., Fractional Differential Equations (1999), Academic Press: Academic Press San Diego · Zbl 0918.34010
[2] Miller, K. S.; Boss, B., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), John Wiley: John Wiley New York · Zbl 0789.26002
[3] Oldham, K. B.; Spanier, J., The Fractional Calculus (1974), Academic Press: Academic Press New York-London · Zbl 0428.26004
[4] Friedrich, C., Relaxation and retardation functions of the Maxwell model with fractional derivatives, Rheologica Acta., 30, 151-158 (1991)
[5] Chen, Y. Q.; Moore, K. L., Analytical stability bounded for a class of delayed fractional-order dynamic systems, Nonlinear Dynam., 29, 191-200 (2002) · Zbl 1020.34064
[6] Ahmad, B.; Sivasundaram, S., Existence results for nonlinear implusive hybrid boundary value problems involving fractional differential equations, Nonlinear Anal. Hybrid Syst., 3, 3, 251-258 (2009) · Zbl 1193.34056
[7] Odibat, Z. M., Analytic study on linear systems of fractional differential equations, Comput. Math. Appl., 59, 3, 1171-1183 (2010) · Zbl 1189.34017
[8] Lin, W., Global existence and chaos control of fractional differential equations, J. Math. Anal. Appl., 332, 709-726 (2007) · Zbl 1113.37016
[9] Wen, X. J.; Wu, Zh. M.; Lu, J. G., Stability analysis of a class of nonlinear fractional-order systems, IEEE Trans. Circuits Syst. II, Express. Briefs, 55, 11, 1178-1182 (2008)
[10] E. Bazhlekova, Fractional Evolution Equations in Banach Spaces, Ph.D. Thesis, Eindhoven University of Technology, 2001.; E. Bazhlekova, Fractional Evolution Equations in Banach Spaces, Ph.D. Thesis, Eindhoven University of Technology, 2001. · Zbl 0989.34002
[11] Henry, D., (Geometric Theory of Semilinear Parabolic Equations. Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 840 (1981), Springer-Verlag: Springer-Verlag New York, Berlin) · Zbl 0456.35001
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