Research Article
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Interval oscillation criteria for impulsive conformable fractional differential equations

Year 2020, Volume: 69 Issue: 1, 815 - 831, 30.06.2020
https://doi.org/10.31801/cfsuasmas.438566

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.

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.
Year 2020, Volume: 69 Issue: 1, 815 - 831, 30.06.2020
https://doi.org/10.31801/cfsuasmas.438566

Abstract

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.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Thangaraj Raja 0000-0002-1829-1729

Yasar Bolat 0000-0002-7978-1078

Kandhasamy Logaarası This is me 0000-0002-6154-746X

Vadivel Sadhasivam 0000-0001-5333-0001

Publication Date June 30, 2020
Submission Date June 29, 2018
Acceptance Date April 20, 2020
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Raja, T., Bolat, Y., Logaarası, K., Sadhasivam, V. (2020). Interval oscillation criteria for impulsive conformable fractional differential equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 815-831. https://doi.org/10.31801/cfsuasmas.438566
AMA Raja T, Bolat Y, Logaarası K, Sadhasivam V. Interval oscillation criteria for impulsive conformable fractional differential equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):815-831. doi:10.31801/cfsuasmas.438566
Chicago Raja, Thangaraj, Yasar Bolat, Kandhasamy Logaarası, and Vadivel Sadhasivam. “Interval Oscillation Criteria for Impulsive Conformable Fractional Differential Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 815-31. https://doi.org/10.31801/cfsuasmas.438566.
EndNote Raja T, Bolat Y, Logaarası K, Sadhasivam V (June 1, 2020) Interval oscillation criteria for impulsive conformable fractional differential equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 815–831.
IEEE T. Raja, Y. Bolat, K. Logaarası, and V. Sadhasivam, “Interval oscillation criteria for impulsive conformable fractional differential equations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 815–831, 2020, doi: 10.31801/cfsuasmas.438566.
ISNAD Raja, Thangaraj et al. “Interval Oscillation Criteria for Impulsive Conformable Fractional Differential Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 815-831. https://doi.org/10.31801/cfsuasmas.438566.
JAMA Raja T, Bolat Y, Logaarası K, Sadhasivam V. Interval oscillation criteria for impulsive conformable fractional differential equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:815–831.
MLA Raja, Thangaraj et al. “Interval Oscillation Criteria for Impulsive Conformable Fractional Differential Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 815-31, doi:10.31801/cfsuasmas.438566.
Vancouver Raja T, Bolat Y, Logaarası K, Sadhasivam V. Interval oscillation criteria for impulsive conformable fractional differential equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):815-31.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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