Oscillation of fractional order functional differential equations
with nonlinear damping

• Authors: Mustafa Bayram , Hakan Adiguzel , Suleyman Ogrekci
• 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.

Keywords

EN

fractional derivative; fractional differentialequation; Riemann-Liouville derivative; Riccati transformation; oscillation criteria

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2015
• Volume: 13
• Issue: 1

Dates

received

14 - 11 - 2015

accepted

27 - 11 - 2015

online

31 - 12 - 2015

Contributors

author

Mustafa Bayram

• Department of health
  Sciences, Uskudar University, Uskudar, Istanbul, Turkey

author

Hakan Adiguzel

• Department of Mathematical Engineering,
  Yildiz Technical University Istanbul, Turkey

author

Suleyman Ogrekci

• Department of Mathematics, Amasya University,
  Amasya, Turkey

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)

Identifiers

DOI

10.1515/phys-2015-0053