×

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.
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Podlubny, I., Fractional differential equations, (1999), 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 New York
[3] Oldham, K.B.; Spanier, J., The fractional calculus, (1974), 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.
[11] Henry, D., ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.