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Oscillation of Fractional Nonlinear Difference Equations

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Abstract (2. Language): 
The oscillation criteria for forced nonlinear fractional difference equa- tion of the form A x(t) + f1(t, x(t + )) =v(t) + f2(t, x(t + )), t ∈ N0, 0 < ≤ 1, A −1x(t)|t=0 =x0, where A denotes the Riemann-Liouville like discrete fractional differ- ence operator of order is presented.
805-813

REFERENCES

References: 

[1] G.A. Anastassiou, Discrete fractional calculus and inequalities,
http://arxiv.org/abs/0911.3370v1.
[2] F. M. Atici and P. W. Eloe, Initial value problems in discrete fractional
calculus, Proceedings of the American Mathematical Society, Vol. 137,
No. 3, pp. 981-989, 2009.
[3] F. M. Atici and P. W. Eloe, A transform method in discrete fractional
calculus, International Journal of Difference Equations, Vol. 2, No. 2, pp.
165-176, 2007.
[4] F. M.Atici and P. W. Eloe, Discrete fractional calculus with the nabla op-
erator, Electronic Journal of Qualitative Theory of Differential Equations,
No. 3, pp. 1-12, 2009.
[5] Da-Xue Chen, Oscillation criteria of fractional differential equations, Ad-
vances in Difference Equations, 2012, 2012:33.
[6] K. Diethelm, The Analysis of Fractional Differential Equations, Springer,
Berlin, 2010.
[7] Fulai Chen, Zhigang Liu, Asymptotic Stability Results for Nonlinear Frac-
tional Difference Equations, Hindawi Publishing Corporation, Journal of
Applied Mathematics, Volume 2012, Article ID 879657, 14 pages.
[8] F. Chen, Fixed points and asymptotic stability of nonlinear fractional dif-
ference equations, Electronic Journal of Qualitative Theory of Differential
Equations, Vol. 39, pp. 1-18, 2011.
[9] Fulai Chen, Xiannan Luo, Yong Zhou, Existence Results for Nonlinear
Fractional Difference Equation, Hindawi Publishing Corporation, Ad-
vances in Difference Equations, Volume 2011, Article ID 713201, 12 pages.
[10] G.H. Hardy, J.E. Littlewood, G. P´olya, Inequalities, Cambridge Univer-
sity Press, Cambridge (1959).
[11] Holm, Michael T., The Theory of Discrete Fractional Calculus: Devel-
opment and Application (2011), Dissertations, Theses, and Student Re-
search Papers in Mathematics. Paper 27.
Oscillation of Fractional Nonlinear Difference Equations 813
[12] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of
Fractional Differential Equations. North-Holland Math. Studies 204, El-
sevier, Amsterdam, 2006.
[13] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and
Fractional Differential Equations, John Wiley & Sons, New York, NY,
USA, 1993.
[14] I.Petras, Control of Fractional-Order Chua’s System,
arXiv:nlin/0008029v1.
[15] I. Podlubny, Fractional Differential Equations, Academic Press, San
Diego, Calif, USA, 1999.
[16] Radek Matusu, Application of fractional order calculus to control theory,
International Journal of Mathematical Models and Methods in Applied
Sciences, Issue 7, Volume 5, 2011.
[17] Said R. Grace, Ravi P. Agarwal, Patricia J.Y. Wong, A˘gacik Zafer, On
the Oscillation of Fractional Differential Equations, Fractional Calculus
and Applied Analysis, Volume 15, Number 2 (2012).

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