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

Published online by Cambridge University Press:  08 July 2016

Shuiping Yang*
Department of Mathematics, Huizhou University, Guangdong 516007, China
*Corresponding author. (S. P. Yang)
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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.

Research Article
Copyright © Global-Science Press 2016 

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[1]Diethelm, Kai, Analysis of fractional differential equations, J. Math. Anal. Appl., 265 (2002), pp. 229248.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. 548560.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. 115124.Google Scholar
[4]Lakshmikantham, V., Theory of fractional functional differential equations, Nonlinear Anal. Theory Methods Appl., 69 (10) (2008), pp. 33373343.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. 885898.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. 715727.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. 1529.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. 672688.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. 2931.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. 586597.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. 10751081.CrossRefGoogle Scholar