SavedAdd your journal

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

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

Jehad ALZABUT
Bahaa El-Din ABDALLAH
Thabet ABDELJAWAD
Pages
207–217
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Ourresults improve those obtained in the previous works.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Based on certain mathematical inequalities and Volterra sum equations, we establish oscillation criteria for higher order fractional difference equations with mixed nonlinearities.
📊
Key Findings & Data:Two examples are constructed to demonstrate the validity of the proposed assumptions.
💡
Conclusion & Impact:Ourresults improve those obtained in the previous works.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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. Ourresults improve those obtained in the previous works.

🔖

Cite This Article

ALZABUT, J., ABDALLAH, B. E., ABDELJAWAD, T. (2022). 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/528354

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (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 En-gineering, Academiv Press,
  11. San Diego, Calif., USA, 1999. R. Hilfer: Applications of Fractional Calculus in Physics, World Scientific Publishing Com-pany, 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 nonlinear force