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Symmetry 2018, 10(12), 769; https://doi.org/10.3390/sym10120769

Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems

1
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
2
Department of Electrical and Electronic Engineering, Istanbul Gelisim University, Avcilar, Istanbul 34310, Turkey
3
Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Periyar University), Rasipuram 637 401, Namakkal Dt., India
*
Author to whom correspondence should be addressed.
Received: 18 October 2018 / Revised: 4 December 2018 / Accepted: 11 December 2018 / Published: 18 December 2018
(This article belongs to the Special Issue Fractional Differential Equations: Theory, Methods and Applications)
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Abstract

In the present work we study the oscillatory behavior of three dimensional α -fractional nonlinear delay differential system. We establish some sufficient conditions that will ensure all solutions are either oscillatory or converges to zero, by using the inequality technique and generalized Riccati transformation. The newly derived criterion are also used to establish a new class of systems with delay which are not covered in the existing study of literature. Further, we constructed some suitable illustrations. View Full-Text
Keywords: oscillation; nonlinear differential system; delay differential system; α-fractional derivative oscillation; nonlinear differential system; delay differential system; α-fractional derivative
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kilicman, A.; Sadhasivam, V.; Deepa, M.; Nagajothi, N. Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems. Symmetry 2018, 10, 769.

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