EXISTENCE OF NONOSCILLATORY SOLUTIONS FOR SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS

Youjun Liu; Huanhuan Zhao; Huiqin Chen; Shugui Kang

doi:10.11948/20190012

2019 Volume 9 Issue 5

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Youjun Liu, Huanhuan Zhao, Huiqin Chen, Shugui Kang. EXISTENCE OF NONOSCILLATORY SOLUTIONS FOR SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1940-1947. doi: 10.11948/20190012

Citation:

Youjun Liu, Huanhuan Zhao, Huiqin Chen, Shugui Kang. EXISTENCE OF NONOSCILLATORY SOLUTIONS FOR SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1940-1947. doi: 10.11948/20190012

EXISTENCE OF NONOSCILLATORY SOLUTIONS FOR SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS

1.
School of Mathematics and Statistics, Shanxi Datong University Datong, Shanxi 037009, China

Corresponding author: Email address:lyj9791@126.com(Y. Liu)
Fund Project: The authors were supported by National Natural Science Foundation of China (11871314, 61803241), Natural Sciences Foundation of Shanxi Province (201801D121001), Natural Sciences Foundation of Datong City (2017125, 2018146), ScientificResearch Start-up Funding of Doctor of Shanxi Datong University (2015-B-07), 131 Talent Project at Shanxi Province and Scientific Research Project of Shanxi Datong University (2017K4)

Abstract

Abstract

In this paper we consider the system of fractional differential equations with positive and negative coefficients. We use the Banach contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.
- System /
- fractional differential equation /
- Liouville derivative /
- positive and negative coefficients /
- nonoscillatory solutions.
MSC: 34A08, 34K11, 35K99

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References

[1]	R. P. Agarwal, M. Bohner, W. T. Li, Nonoscillation and Oscillation: Theory for Functional Differential Equations, Marcel Dekker Inc, New York, 2004. Google Scholar
[2]	T. Candan, Existence of nonoscillatory solutions for system of higher order nonliear neutral differential equations, Mathematical and Computer Modelling, 2013, 57, 375-381. doi: 10.1016/j.mcm.2012.06.016 CrossRef Google Scholar
[3]	K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010. Google Scholar
[4]	L. H. Erbe, Q. K. Kong, B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker Inc, New York, 1995. Google Scholar
[5]	I. Györi, G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Presss, Oxford, 1991. Google Scholar
[6]	K. Gopalsamy, Stability and Oscillation in Delay Differential Equations of Population Dynamics, Kluwer Academic, Boston, 1992. Google Scholar
[7]	G. S. Ladde, V. Lakshmikantham, B. G. Zhang, Oscillation Theory of Differential Equations with Deviation Arguments, Dekker, New York, 1989. Google Scholar
[8]	A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, In: North-Holland Mathematics Studies, vol. 204. Elsevier Science B.V., Amsterdam, 2006. Google Scholar
[9]	I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. Google Scholar
[10]	Y. Zhou, B. Ahmad, A. Alsaedi, Existence of nonoscillatory solutions for fractional functional differential equations, Bulletin of the Malaysian Mathematical Sciences Society, 2017, 2017, 1-16. Google Scholar
[11]	Y. Zhou, B. Ahmad, A. Alsaedi, Existence of nonoscillatory solutions for fractional neutral differential equations, Appl. Math. Lett., 2017, 72, 70-74. doi: 10.1016/j.aml.2017.04.016 CrossRef Google Scholar
[12]	Y. Zhou, L. Peng, On the time-fractional Navier-Stokes equations, Comput. Math. Appl. 2017, 73(6), 874-891. doi: 10.1016/j.camwa.2016.03.026 CrossRef Google Scholar
[13]	Y. Zhou, L. Peng, Weak solutions of the time-fractional Navier-Stokes equations and optimal control, Comput. Math. Appl., 2017, 73(6), 1016-1027. doi: 10.1016/j.camwa.2016.07.007 CrossRef Google Scholar
[14]	Y. Zhou, L. Zhang, Existence and multiplicity results of homoclinic solutions for fractional Hamiltonian systems, Comput. Math. Appl., 2017, 73(6), 1325-1345. doi: 10.1016/j.camwa.2016.04.041 CrossRef Google Scholar