PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2015 | 13 | 1 |
Article title

Oscillation of fractional order functional differential equations
with nonlinear damping

Content
Title variants
Languages of publication
EN
Abstracts
EN
In this paper, we are concerned with the oscillatory
behavior of a class of fractional differential equations
with functional terms. The fractional derivative is defined
in the sense of the modified Riemann-Liouville derivative.
Based on a certain variable transformation, by using a generalized
Riccati transformation, generalized Philos type
kernels, and averaging techniques we establish new interval
oscillation criteria. Illustrative examples are also given.
Publisher
Journal
Year
Volume
13
Issue
1
Physical description
Dates
received
14 - 11 - 2015
accepted
27 - 11 - 2015
online
31 - 12 - 2015
References
  • [1] S. Das, Functional Fractional Calculus for System Identificationand Controls, Springer, New York (2008)
  • [2] K. Diethelm, A. Freed, On the solution of nonlinear fractionalorder differential equations used in the modeling of viscoplasticity,In: F. Keil, W. Mackens, H. Vob, J. Werther (Eds.) Scientific Computing in Chemical Engineering II: ComputationalFluid Dynamics, Reaction Engineering and Molecular Properties,Springer, Heidelberg (1999), 217-224
  • [3] L. Gaul, P. Klein, S. Kempfle, Mech. Syst. Signal Process. 5, 81(1991)
  • [4] W. Glöckle, T. Nonnenmacher, Biophys. J. 68, 46 (1995)
  • [5] F. Mainardi, Fractional calculus: some basic problems in continuumand statistical mechanics, In: A. Carpinteri, F. Mainardi(Eds.), Fractals and Fractional Calculus in Continuum Mechanics,Springer, Vienna (1997), 291-348 .
  • [6] R. Metzler,W. Schick, H. Kilian, T. Nonnenmacher, J. Chem. Phys.103, 7180 (1995)
  • [7] K. Diethelm, The Analysis of Fractional Differential Equations,Springer, Berlin (2010)[WoS]
  • [8] K. Miller, B. Ross, An Introduction to the Fractional Calculus andFractional Differential Equations, Wiley, New York (1993)
  • [9] I. Podlubny, Fractional Differential Equations, Academic Press,San Diego (1999)
  • [10] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications ofFractional Differential Equations, Elsevier, Amsterdam (2006)
  • [11] D. Delbosco, L. Rodino, J. Math. Anal. Appl. 204, 609 (1996)
  • [12] Z. Bai, H. Lü, J. Math. Anal. Appl. 311, 495 (2005)
  • [13] H. Jafari, V. Daftardar-Gejji, Appl. Math. Comput. 180, 700(2006)
  • [14] S. Sun, Y. Zhao, Z. Han, Y. Li, Commun. Nonlinear Sci. Numer.Simul. 17, 4961 (2012)
  • [15] M. Muslim, Math. Comput. Model. 49, 1164 (2009)
  • [16] A. Saadatmandi, M. Dehghan, Comput. Math. Appl. 59, 1326(2010)
  • [17] F. Ghoreishi, S. Yazdani, Comput. Math. Appl. 61, 30 (2011)
  • [18] J. Edwards, N. Ford, A. Simpson, J. Comput. Appl.Math. 148, 401(2002)
  • [19] L. Galeone, R. Garrappa, J. Comput. Appl.Math. 228, 548 (2009)
  • [20] J. Trigeassou, N.Maamri, J.A. Sabatier, A. Oustaloup, Signal Process.91, 437 (2011)
  • [21] W. Deng, Nonlinear Anal. 72, 1768 (2010)
  • [22] R.P. Agarwal, S.R. Grace, D. O’Regan, Oscillation Theory forSecond Order Linear, Half Linear, Super Linear and Sub LinearDynamic Equations, Kluwer Academic Publishers, The Netherlands,672pp. (2002)
  • [23] R.P. Agarwal, M. Bohner, L. Wan-Tong, Nonoscillation and Oscillation:Theory for Functional Differential Equations, MarcelDekker Inc., New York, 376pp. (2004)
  • [24] G. Jumarie, Comput. Math. Appl. 51, 1367 (2006)
  • [25] G. Jumarie, Appl. Math. Lett. 22, 378 (2009)[Crossref]
  • [26] N. Faraz, Y. Khan, H. Jafari, A. Yildirim, M. Madani, J. King. SaudUniv. 23, 413 (2011)
  • [27] B. Lu, Phys. Lett. A 376, 2045 (2012)
  • [28] Q. Feng, F. Meng, Electr. J. Differ. Equ. 2013, 1 (2013)
  • [29] T. Liu, B. Zheng, F. Meng,Math. Probl. Eng. 2013, 830836 (2013)
  • [30] H. Qin, B. Zheng, Scientific World J. 2013, 685621 (2013)
  • [31] Q. Feng, IAENG IJAM 43, IJAM_43_3_09 (2013)
  • [32] S.M. Guo, L. Mei, Y. Li, Y.F. Sun, Phys. Lett. A 376, 407 (2012)
  • [33] S. Zhang, H. Zhang, Phys. Lett. A 375, 1069 (2011)
  • [34] Y. Huang, F. Meng, Appl. Math. Comput. 199, 644 (2008)
  • [35] G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, second ed.,Cambridge University Press, Cambridge (1988)
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_1515_phys-2015-0053
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.