Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T21:04:50.632Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: General theory in ordinary differential equations Functional-differential and differential-difference equations

Published online by Cambridge University Press:  08 July 2016

Shuiping Yang
Shuiping Yang*
Affiliation:
Department of Mathematics, Huizhou University, Guangdong 516007, China
*
*Corresponding author. Email:yang52053052@163.com (S. P. Yang)
Get access

Abstract

In this paper, we discuss the dependence of the solutions on the parameters (order, initial function, right-hand function) of fractional neutral delay differential equations (FNDDEs). The corresponding theoretical results are given respectively. Furthermore, we present some numerical results that support our theoretical analysis.

Keywords

Fractional neutral delay differential equationsCaputo fractional derivativedependence

MSC classification

Secondary: 34A08: Fractional differential equations 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 34K40: Neutral equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 5 , October 2016 , pp. 772 - 783
Copyright
Copyright © Global-Science Press 2016 

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]Diethelm, Kai, Analysis of fractional differential equations, J. Math. Anal. Appl., 265 (2002), pp. 229–248.CrossRefGoogle Scholar
[2]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.CrossRefGoogle Scholar
[3]Jiang, Yingjun and Ma, Jingtang, Spectral collocation methods for Volterra-integro differential equations with noncompact kernels, J. Comput. Appl. Math., 244 (2013), pp. 115–124.Google Scholar
[4]Lakshmikantham, V., Theory of fractional functional differential equations, Nonlinear Anal. Theory Methods Appl., 69 (10) (2008), pp. 3337–3343.CrossRefGoogle Scholar
[5]Podlubny, I., Fractional Differential Equations, Academic Press, SanDiego, 1999.Google Scholar
[6]Tarasov, Vasily E. and Zaslavsky, George M., Fractional dynamics of systems with long-range interaction, Commun. Nonlinear Sci. Numer. Simul., 11(8) (2006), pp. 885–898.Google Scholar
[7]Uchaikin, Vladimir V. and Sibatov, Renat T., Fractional theory for transport in disordered semiconductors, Commun. Nonlinear Sci. Numer. Simul., 13(4) (2008), pp. 715–727.CrossRefGoogle Scholar
[8]Wei, Yunxia and Chen, Yanping, Legendre spectral collocation method for neutral and high-order Volterra integro-differential equation, Appl. Numer. Math., 81 (2014), pp. 15–29.Google Scholar
[9]Wei, Yunxia and Chen, Yanping, Legendre spectral collocation methods for pantograph volterra delay-integro-differential dquations, J. Sci. Comput., 53 (2012), pp. 672–688.CrossRefGoogle Scholar
[10]Weilbeer, M., Efficient Numerical Methods for Fractional Differential Equations and Their Analytical Background, Papierflieger, 2006.Google Scholar
[11]Yang, S. P., The existence of solutions for multi-order fractional differential delay equation, Journal of Huizhou University (Natural Science Edition), 3 (2011), pp. 29–31.Google Scholar
[12]Yang, S. P., Xiao, A. G. and Pan, X. Y., Dependence analysis of the solutions on the parameters of fractional delay differential equations, Adv. Appl. Math. Mech., 3(5) (2011), pp. 586–597.CrossRefGoogle Scholar
[13]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.CrossRefGoogle Scholar