Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-17T03:48:37.225Z Has data issue: false hasContentIssue false
  • English
  • Français

Dependence Analysis of the Solutions on the Parameters of Fractional Delay Differential Equations

Published online by Cambridge University Press:  03 June 2015

Shuiping Yang ,
Aiguo Xiao  and
Xinyuan Pan
Shuiping Yang*
Affiliation:
School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China Department of Mathematics, Huizhou University, Guangdong 516007, China
Aiguo Xiao*
Affiliation:
School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China
Xinyuan Pan*
Affiliation:
School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China
*
Email: yang52053052@yahoo.com.cn
Corresponding author. Email: xag@xtu.edu.cn
Email: panxinyuan198312@163.com
Get access

Abstract

In this paper, we investigate the dependence of the solutions on the parameters (order, initial function, right-hand function) of fractional delay differential equations (FDDEs) with the Caputo fractional derivative. Some results including an estimate of the solutions of FDDEs are given respectively. Theoretical results are verified by some numerical examples.

Keywords

34A0834A1034A1234K37Fractional delay differential equationCaputo fractional derivativedependence
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 5 , October 2011 , pp. 586 - 597
Copyright
Copyright © Global-Science Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Delbosco, D. and Rodino, L., Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204 (1996), pp. 609–625.CrossRefGoogle Scholar
[2] He, J. H., Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Tech., 15(2) (1999), pp. 86–90.Google Scholar
[3] Uchaikin, V. V. and Sibatov, R. T., Fractional theory for transport in disordered semiconductors, Commun. Nonlinear. Sci. Numer. Simul., 13(4) (2008), pp. 715–727.Google Scholar
[4] Tarasov, V. E. and Zaslavsky, G. M., Fractional dynamics of systems with long-range interaction, Commun. Nonlinear. Sci. Numer. Simul., 11(8) (2006), pp. 885–898.Google Scholar
[5] Weilbeer, M., Efficient Numerical Methods for Fractional Differential Equations and Their Analytical Background, Papierflieger, 2006.Google Scholar
[6] Podlubny, I., Fractional Differential Equations, Academic Press, SanDiego, 1999.Google Scholar
[7] Lakshmikantham, V., Theory of fractional functional differential equations, Nonlinear. Anal-Theor., 69(10) (2008), pp. 3337–3343.Google Scholar
[8] Ye, H. P., Gao, J. M. and Ding, Y. S., A generalized Gronwall inequality and its application to a fractional differential equation, J. Math. Anal. Appl., 328 (2007), pp. 1075–1081.Google Scholar
[9] Diethelm, K., Analysis of fractional differential equations, J. Math. Anal. Appl., 265 (2002), pp. 229–248.Google Scholar
[10] Galeone, L. and Garrappa, R., Explicit methods for fractional differential equations and their stability properties, J. Comput. Appl. Math., 228(2) (2009), pp. 548–560.Google Scholar