KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 2

On the oscillation of higher order fractional difference equations with mixed nonlinearities

Bahaaeldin ABDALLA
Jehad ALZABUT
Thabet ABDELJAWAD
Sayfa
207–217
Yayın Tarihi
2018-04-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Our results improve those obtained in the previous works.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Based on certain mathematical inequalities and Volterra sum equations, we establish oscillation criteria for higher order fractional difference equations with mixed nonlinearities.
📊
Temel Bulgular & Veri:Two examples are constructed to demonstrate the validity of the proposed assumptions.
💡
Sonuç & Katkı:Our results improve those obtained in the previous works.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Oscillation of solutions · Fractional difference equations · Mixed nonlinearities

Abstract

Based on certain mathematical inequalities and Volterra sum equations, we establish oscillation criteria for higher order fractional difference equations with mixed nonlinearities. The problem is addressed for equations involving Riemann-Liouville and Caputo operators. Two examples are constructed to demonstrate the validity of the proposed assumptions. Our results improve those obtained in the previous works.

🔖

Bu Makaleye Atıf Yap

ABDALLA, B., ALZABUT, J., ABDELJAWAD, T. (2018). On the oscillation of higher order fractional difference equations with mixed nonlinearities. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 2, 207–217. https://ajindex.com/articles/669444

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (12)

  1. R. P. Agarwal, S. R. Grace, D. O’Regan: Oscillation Theory for Second Order Linear, Half–Linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic Publishers, 2002.
  2. R. P. Agarwal, M. Bohner, W.-T. Li: Nonoscillation and Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, 2004.
  3. R. P. Agarwal, M. Bohner, S. R. Grace, D. O’Regan: Discrete Oscillation Theory, Hindawi Publishing Corporation, 2005. S. H. Saker: Oscillation Theory of Delay Differential and Difference Equations: Second and Third Orders, Verlag Dr. Müller, 2010.
  4. Y. Sun, J. S. W. Wong: Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007), 549–560.
  5. R. P. Agarwal, M. Bohner, W.-S. Cheung, S. R. Grace: Oscillation criteria for forced second order differential equations with mixed nonlinearities, Math. Comput. Modelling 45 (2007), 965–973.
  6. Z. Zhang, X.Wang, H. Han: Oscillation criteria for forced second order differential equations with mixed nonlinearities, Appl. Math. Lett. 22 (7) (2009), 1096–1101.
  7. L. Erbe, T. S. Hassan, A. Peterson: Oscillation of third–order functional dynamic equations with mixed nonlinearities on time scales, J. Appl. math. Comput. 34 (2010), 353–371.
  8. T. S. Hassan, L. Erbe, A. Peterson: Forced oscillation of second order differential equations with mixed nonlinearities, Acta Math. Sci. Ser. B Engl. Ed. 31 (2) (2011). 613–626.
  9. A. Özbekler, A. Zafer: Second order oscillation of mixed nonlinear dynamic equations with several positive and negative coefficients, Duscrete Contin. Dyn. Syst. Suppl. 2011, 1167– 1175. Z. Xu, A. Cheng: Oscillation of second order differential equations with mixed nonlinearities, Turk J. Math. 38 (2014), 688–705.
  10. S. G. Samko, A. A. Kilbas, O. I. Marichev: Fractional Intergrals and Derivatives: Theory and Applications, Gordon and Beach Science, Yverdon, Switzerland, 1993. I. Podlubny: Fractional Diffeential Equations, vol. 198 of Mathematics in Science and Engineering, Academiv Press,
  11. San Diego, Calif., USA, 1999. R. Hilfer: Applications of Fractional Calculus in Physics, World Scientific Publishing Company, Singapore, 2000.
  12. S. R. Grace, R. P. Agarwal, P. J. Y. Wong, A. Zafer: On the oscillation of fractional differential equations, Fract. Calc. Appl. Anal. 15 (2) (2012), 222–231. D.-X. Chen: Oscillation criteria of fractional differential equations, Adv. Difference Equ. 2012, 2012:33. Q. Feng, F. Meng: Oscillation of solutions to nonl