Kesirli Nötral Diferensiyel Denklemlerin Çözümlerinin Kalitatif Davranışları Üzerine

Year 2018, Volume: 30 Issue: 3, 211 - 217, 30.09.2018

Hakan Adıgüzel

https://doi.org/10.7240/marufbd.425858

Abstract

.Bu çalışmada, kesirli nötral diferensiyel denklemlerin bir sınıfı
dikkate alınmıştır. Yeni karşılaştırma teoremlerine dayanarak, salınımlılık
sonuçları elde edilmiştir. Elde edilen sonuçlar literatürdeki çalışmaları
tamamlamış ve genelleştirmiştir

Keywords

Salınım, Kesirli Türev, Kesirli Diferensiyel Denklemler, Nötral

References

• Kiryakova, V., Generalized fractional calculus and applications, Longman Group UK Limited, Essex (1994).
• Magin, R. L. (2006). Fractional calculus in bioengineering (pp. 269-355). Redding: Begell House.
• Bai, Z., & Xu, R. (2018). The Asymptotic Behavior of Solutions for a Class of Nonlinear Fractional Difference Equations with Damping Term. Discrete Dynamics in Nature and Society, 2018.
• Bayram, M., Adiguzel, H., & Ogrekci, S. (2015). Oscillation of fractional order functional differential equations with nonlinear damping. Open Physics, 13(1).
• Agarwal, R. P., Lakshmikantham, V., & Nieto, J. J. (2010). On the concept of solution for fractional differential equations with uncertainty. Nonlinear Analysis: Theory, Methods & Applications, 72(6), 2859-2862.
• Secer, A., & Adiguzel, H. (2016). Oscillation of solutions for a class of nonlinear fractional difference equations. The Journal of Nonlinear Science and Applications (JNSA), 9(11), 5862-5869.
• Chen, D. X. (2012). Oscillation criteria of fractional differential equations. Advances in Difference Equations, 2012(1), 33.
• Matignon, D. (1996, July). Stability results for fractional differential equations with applications to control processing. In Computational engineering in systems applications (Vol. 2, pp. 963-968). Lille, France: IMACS, IEEE-SMC.
• Öğrekçi, S. (2015). Generalized Taylor series method for solving nonlinear fractional differential equations with modified Riemann-Liouville derivative. Advances in Mathematical Physics, 2015.
• Öğrekçi, S. (2015). Interval oscillation criteria for functional differential equations of fractional order. Advances in Difference Equations, 2015(1), 3.
• Muthulakshmi, V., & Pavithra, S. (2017). Interval Oscillation Criteria for Forced Fractional Differential Equations with Mixed Nonlinearities. Global Journal of Pure and Applied Mathematics, 13(9), 6343-6353.
• Wang, Y. Z., Han, Z. L., Zhao, P., & Sun, S. R. (2015). Oscillation theorems for fractional neutral differential equations. Hacettepe journal of mathematics and statistics, 44(6), 1477-1488.
• Ganesan, V., & Kumar, M. S. (2016). Oscillation theorems for fractional order neutral differential equations. Journal of Applied Computer Science & Mathematics (revised).
• Jumarie, G. (2006). Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Computers & Mathematics with Applications, 51(9-10), 1367-1376.
• Li, T., & Rogovchenko, Y. V. (2015). Oscillation of second‐order neutral differential equations. Mathematische Nachrichten, 288(10), 1150-1162.
• Philos, C. G. (1981). On the existence of nonoscillatory solutions tending to zero at∞ for differential equations with positive delays. Archiv der Mathematik, 36(1), 168-178.
• Kitamura, Y., & Kusano, T. (1980). Oscillation of first-order nonlinear differential equations with deviating arguments. Proceedings of the American Mathematical Society, 64-68.