Oscillation of solutions to a generalized forced nonlinear conformable fractional differential equation

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2019-03-0028

Keywords:

Oscillation, Forced, Nonlinear conformable fractional differential equation

Abstract

By using averaging functions, we present some new oscillation criteria for the solution of a generalized forced nonlinear conformable fractional differential equation. The results obtained here extend and improve on some existing results. Examples are also given to show the validity of our results.

Author Biographies

A. M. Ogunbanjo, University of Ibadan.

Department of Mathematics.

P. O. Arawomo, University of Ibadan.

Department of Mathematics.

References

T. Abdeljawad, “On conformable fractional calculus”, Journal of Computational and Applied Mathematics, vol. 279, pp. 57–66, 2015, doi: 10.1016/j.cam.2014.10.016.

F. Zulfeqarr, A. Ujlayan, and P. Ahuja, “A new fractional derivative and its fractional integral with some example”, Apr. 2017. arXiv:1705.00962.

Q. Feng, “Interval Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Nonlinear Damping Term”, IAENG International Journal of Applied Mathematics, vol. 43, no. 3, pp. 154–159, Aug. 2013. [On line]. Available: http://bit.ly/31iDarg

F. Usta and M. Z. Sarıkaya, “Explicit bounds on certain integral inequalities via conformable fractional calculus”, Cogent Mathematics, vol. 4, no. 1, 2017, doi: 10.1080/23311835.2016.1277505.

S. Grace and B. Lalli, “Oscillation theorems for second order superlinear differential equations with damping”, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, vol. 53, no. 2, pp. 156–165, Oct. 1992, doi: 10.1017/s144678870003576x.

J. Wong, “An oscillation theorem for second order sublinear differential equations”, Proceedings of the American Mathematical Society, vol. 110, no. 3, pp. 633–633, 1990, doi: 10.1090/S0002-9939-1990-1000170-4.

J. Tariboon and S. K. Ntouyas, “Oscillation of impulsive conformable fractional differential equations”, Open Mathematics, vol. 14, no. 1, 2016, doi: 10.1515/math-2016-0044.

R. Khalil, M. Horani, A. Yousef, and M. Sababheh, “A new definition of fractional derivative”, Journal of Computational and Applied Mathematics, vol. 264, pp. 65–70, 2014, doi: 10.1016/j.cam.2014.01.002.

M. Kwong and J. Wong, “An application of integral inequality to second order nonlinear oscillation”, Journal of Differential Equations, vol. 46, no. 1, pp. 63–77, 1982, doi: 10.1016/0022-0396(82)90110-3.

M. Sarikaya and F. Usta; “On Comparison Theorems for Conformable Fractional Differential Equations”, International Journal of Analysis and Applications, vol. 12, no. 2, pp. 207-214, 2016. [On line]. Available: http://bit.ly/2yzvdld

M. Remili, “Oscillation criteria for second order nonlinear perturbed differential equations”, Electronic Journal of Qualitative Theory of Differential Equations, no. 25, pp. 1–11, May 2010, doi: 10.14232/ejqtde.2010.1.25.

Q. Feng and F. Meng, “Oscillation of Solutions to Nonlinear forced fractional differential equations”, Electronic Journal of Differential Equations, vol. 2013, no. 169, pp. 1-10, Jul. 2013. [On line]. Available: http://bit.ly/2MBeuq4

R. Agarwal, M. Bohner, and W. Li, Nonoscillation and oscillation: theory for functional differential equations. New York: Marcel Dekker, 2004.

S. Grace, R. Agarwal, P. Wong, and A. Zafer, “On the oscillation of fractional differential equations”, Fractional Calculus and Applied Analysis, vol. 15, no. 2, Mar. 2012, doi: 10.2478/s13540-012-0016-1.

S. Öğrekçi, “Interval oscillation criteria for functional differential equations of fractional order”, Advances in Difference Equations, vol. 2015, no. 1, Jan. 2015, doi: 10.1186/s13662-014-0336-z.

Y. Çenesiz and A. Kurt, “The solutions of time and space conformable fractional heat equations with conformable Fourier transform”, Acta Universitatis Sapientiae, Mathematica, vol. 7, no. 2, pp. 130–140, Feb. 2015, doi: 10.1515/ausm-2015-0009.

Published

2019-08-06

How to Cite

[1]
A. M. Ogunbanjo and P. O. Arawomo, “Oscillation of solutions to a generalized forced nonlinear conformable fractional differential equation”, Proyecciones (Antofagasta, On line), vol. 38, no. 3, pp. 429-445, Aug. 2019.

Issue

Section

Artículos