Interval oscillation criteria for impulsive conformable fractional differential equations

Year 2020, Volume: 69 Issue: 1, 815 - 831, 30.06.2020

Thangaraj Raja , Yasar Bolat , Kandhasamy Logaarası Vadivel Sadhasivam

https://doi.org/10.31801/cfsuasmas.438566

Cited By: 1

Abstract

In this paper, we derive new interval oscillation criteria for impulsive conformable fractional differential equations having fixed moments of impulse actions. The results are extended to a more general class of nonlinear impulsive conformable fractional differential equations. Examples are also given to illustrate the relevance of the result.

Keywords

Oscillation, impulse, conformable fractional differential equations

References

• Bainov, D.D., Simenov, P.S., Impulsive Differential Equations: Periodic Solutions and Applications, Longman, Harlow, 1993.
• Chen, D.X., Oscillation criteria of fractional differential equations, Adv. Diff. Equ., 2012 (2012), 1-10. Chen, D., Qu, P., Lan, Y., Forced oscillation of certain fractional differential equations, Adv. Difference Equ., 2013 (2013),
• Fend, Q., Meng, F., Oscillation of solutions to nonlinear forced fractional differential equations, Electron. J. Differential Equations, 169 (2013), 1-10.
• Grace, S.R., Agarwal, R.P., Wong, P.J.Y., Zafer, A., On the oscillation of fractional differential equations, Frac. Calc. Appl. Anal., 15 (2012), 222-231.
• Han, Z., Zhao, Y., Sun, Y., Zhang, C., Oscillation for a class of fractional differential equation, Discrete Dyn. Nat. Soc., (2013), 1-6. Huang, M., Feng, W.Z., Oscillation of second order impulsive delay differential equations with forcing term, J. Natural Science of Heilongjiang University, 23 (2006), 452-456 (in Chinese).
• Kalaimani, T., Raja, T., Sadhasivam, V., Saker, S.H., Oscillation of Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments, Bul. Math. Soc. Sci. Math. Roumanie Tome, 61(109), (2018), 51-68.
• Khalil, R.R., Horani, M. Al., Yousef, A., Sababheh, M., A new definition of fractional derivative, J. Comupt. Appl. Math., 264 (2014), 65-70. Kilbas, A.A., Srivastava, H. M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
• Kong, Q., Interval criteria for oscillation of second-order linear differential equation, J. Math. Anal. Appl., 229 (1999), 483-492.
• Lakshmikantham, V., Bainov, D.D., Simeonov, P.S., Theory of Impulsive Differential Equations, World Scientific Publishers, Singapore, 1989.
• Li, Q.L., Cheung, W.S., Interval oscillation criteria for second-order forced delay differential equations under impulsive effects, Electron. J. Qual. Theor. Diff. Eq., 2013(43) (2013), 1-11.
• Liu, T., Zheng, B., Meng, F., Oscillation on a class of differential equations of fractional order, Math. Probl. Eng., (2013), 1-13.
• Muthulakshmi, V., Thandapani, E., Interval criteria for oscillation of second-order impulsive differential equation with mixed nonlinearities, Electron. J. Differ. Eq., 2011(40) (2011), 1-14.
• Özbekler, A., Zafer A., Oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations, Comput. Math. Appl., 61 (2011), 933-940.
• Philos, Ch.G., Oscillation theorems for linear differential equations of second order, Arch. Math., 53 (1989), 482-492.
• Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
• Sadhasivam, V., Logaarasi, K., Raja, T., Interval oscillation criteria for impulsive partial differential equations, Int. J. Math. and Appl., 6(1-B) (2018), 229-242. Sadhasivam, V., Raja, T., Logaarasi, K., On the interval oscillation of impulsive partial differential equations with damping term, Int. J. Engg. Sci. Math., 6 (2017), 328-340. Thandapani, E., Manju, E., Pinelas, S., Interval oscillation criteria for second order forced impulsive delay differential equations with damping term, Springer Plus, 5 (2016), 1-16.
• Wang, Y.Z., Han, Z.L., Zhao, P., Sun, S.R., On the oscillation and asymptotic behavior for a kind of fractional differential equations, Adv. Difference Equ., 2014 (2014).
• Xiaoliang, Z., Zhonghai, G., Wu-Sheng, W., Interval oscillation criteria for super-half-linear impulsive differential equations with delay, J. Appl. Math., (2012a).
• Yang, J., Liu, A., Liu, T., Forced oscillation of nonlinear fractional differential equations with damping term, Adv. Diff. Equ., 2015 (2015), 1-7. Zhang, C., Feng, W.Z., Yang, J., Huang, M., Oscillation of second order impulsive nonlinear FDE with forcing term, Appl. Math. Comput., 198 (2008), 271-279.