## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Oscillation properties of solutions of fractional difference equations

**ABSTRACT**

In this article, studied the properties of the oscillation of fractional difference equations, and we obtain some results. The results we obtained are an expansion and further development of highly known results. Then we showed them with examples.

**KEYWORDS**

PAPER SUBMITTED: 2018-10-17

PAPER REVISED: 2018-10-30

PAPER ACCEPTED: 2018-11-26

PUBLISHED ONLINE: 2018-12-16

- Hassan, T. S., Oscillation of third order nonlinear delay dynamic equations on time scales. Mathematical and Computer Modelling, 49, (2009),7-8, pp. 1573-1586.
- Öğrekçi, S., Interval Oscillation Criteria For Second-Order Functional Differential Equations, Sigma, 36,(2018),2, pp. 351-359.
- Misir, A., & Öğrekçi, S., Oscillation Criteria for a Class of Second Order Nonlinear Differential Equations, Gazi University Journal of Science, 29, (2016),4, pp. 923-927.
- Erbe, L., et al, Oscillation of third order nonlinear functional dynamic equations on time scales, Differential Equations and Dynamical Systems, 18,(2010),1-2, pp. 199-227.
- G. E. Chatzarakis, et al, Oscillatory solutions of nonlinear fractional difference equations, Int. J. Diff. Equ., (2018). (in press)
- Bayram, M., et al, Oscillatory behavior of solutions of differential equations with fractional order, Appliead Mathematics & Information Sciences, 11, (2017), 3, pp. 683-691.
- Bayram, M., et al, On the oscillation of fractional order nonlinear differential equations, Sakarya University Journal of Science, 21, (2017), 6, pp. 1-20.
- Erbe, L., et al, Oscillation of third order functional dynamic equations with mixed arguments on time scales, Journal of Applied Mathematics and Computing, 34 (2010),1-2, pp. 353-371.
- Secer, A., & Adiguzel, H., , Oscillation of solutions for a class of nonlinear fractional difference equations, The Journal of Nonlinear Science and Applications, 9, (2016),11, pp. 5862-5869.
- Bai, Z., & Xu, R., The asymptotic behavior of solutions for a class of nonlinear fractional difference equations with damping term, Discrete Dynamics in Nature and Society, 2018, (2018).
- Baculíková, B., & Džurina, J., Oscillation of third-order neutral differential equations, Mathematical and Computer Modelling, 52, (2010),1-2, pp. 215-226.
- Chen, D.-X., Oscillation criteria of fractional differential equations, Advances in Difference Equations, 2012, (2012), article 33, 18 pages.
- Liu, T., et al, Oscillation on a class of differential equations of fractional order, Mathematical Problems in Engineering, 2013, (2013).
- Feng, Q., Oscillatory Criteria For Two Fractional Differential Equations, WSEAS Transactions on Mathematics, 13, (2014), pp. 800-810.
- Qin, H., Zheng, B., Oscillation of a class of fractional differential equations with damping term, Sci. World J. 2013, (2013), Article ID 685621.
- Ogrekci, S., Interval oscillation criteria for functional differential equations of fractional order, Advances in Difference Equations, 2015, (2015), 1.
- Bayram, M., et al, Oscillation of fractional order functional differential equations with nonlinear damping, Open Physics, 13, (2015),1.
- Bayram, M., et al, Oscillation criteria for nonlinear fractional differential equation with damping term, Open Physics,14,(2016),1, pp. 119-128.
- Zheng, B., Oscillation for a class of nonlinear fractional differential equations with damping term, Journal of Advanced Mathematical Studies, 6, (2013), 1, pp. 107--115.
- XU, R. Oscillation Criteria for Nonlinear Fractional Differential Equations, Journal of Applied Mathematics, 2013, Article ID 971357, 7 pages.
- Li, W. N., Forced oscillation criteria for a class of fractional partial differential equations with damping term, Mathematical Problems in Engineering, 2015, (2015).
- Sagayaraj, M. R., et al, On the oscillation of nonlinear fractional difference equations, Math. Aeterna, 4, (2014), pp. 91-99.
- Selvam, A. G. M., et al, Oscillatory behavior of a class of fractional difference equations with damping, International Journal of Applied Mathematical Research, 3, (2014),(3) pp. 220-224.
- Li, W. N., Oscillation results for certain forced fractional difference equations with damping term, Advances in Difference Equations, 1, (2016), pp. 1-9.
- Sagayaraj, M. R., et al, Oscillation Criteria for a Class of Discrete Nonlinear Fractional Equations, Bulletin of Society for Mathematical Services and Standards ISSN, 3, (2014), 1, pp. 27-35.
- Atici, F. M., Eloe, P. W., Initial value problems in discrete fractional calculus, Proceedings of the American Mathematical Society, 137, (2008), 3, pp. 981-989.