SavedAdd your journal

Journals / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 4 Issue: 2

Oscillatory Criteria of Nonlinear Higher Order $\Psi$-Hilfer Fractional Differential Equations

Tuğba Yalçın Uzun(AFYON KOCATEPE ÜNİVERSİTESİ)0000-0002-2619-6094
Pages
—
Publication Date
2021-06-01
🏛️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)

The results obtained in this paper are a generalization of the known results in the literature, and present new results for some fractional derivatives.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the forced oscillatory theory for higher order fractional differential equations with damping term via $\Psi$-Hilfer fractional derivative.
📊
Key Findings & Data:We get sufficient conditions which ensure the oscillation of all solutions and give an illustrative example for our results.
💡
Conclusion & Impact:The results obtained in this paper are a generalization of the known results in the literature, and present new results for some fractional derivatives.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$\Psi$-Hilfer fractional derivative · Damping term · Forced oscillation

Abstract

In this paper, we study the forced oscillatory theory for higher order fractional differential equations with damping term via $\Psi$-Hilfer fractional derivative. We get sufficient conditions which ensure the oscillation of all solutions and give an illustrative example for our results. The $\Psi$-Hilfer fractional derivative according to the choice of the $\Psi$ function is a generalization of the different fractional derivatives defined earlier. The results obtained in this paper are a generalization of the known results in the literature, and present new results for some fractional derivatives.

🔖

Cite This Article

Uzun, T. Y. (2021). Oscillatory Criteria of Nonlinear Higher Order $\Psi$-Hilfer Fractional Differential Equations. Fundamental Journal of Mathematics and Applications, Volume: 4 Issue: 2. https://doi.org/10.33401/fujma.888390

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (29)

  1. T. Li, N. Pintus, G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70(3) (2019), Art. 86, pp. 1-18.
  2. T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differ. Integral Equ., 34(5-6) (2021), 315-336.
  3. M. Javadi, M. A. Noorian, S. Irani, Stability analysis of pipes conveying fluid with fractional viscoelastic model, Meccanica 54 (2019), 399–410. https://doi.org/10.1007/s11012-019-00950-3
  4. I. S. Jesus, J. A. Tenreiro Machado, Application of Integer and Fractional Models in Electrochemical Systems, Math. Prob. Eng., 2012 (2012), Article ID 248175.
  5. F. Ali, N. A. Sheikh, I. Khan, M. Saqib, Magnetic field effect on blood flow of Casson fluid in axisymmetric cylindrical tube: A fractional model, J. Magn. Magn. Mater., 423 (2017), 327-336.
  6. Y. Tang, Y. Zhen, B. Fang, Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid, Appl. Math. Modell., 56 (2018), 123-136.
  7. J. Hadamard, Essai sur letude des fonctions donn´ees par leur d´eveloppement de taylor, Jour. Pure and Appl. Math., 4(8) (1892), 101–186.
  8. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies). Elsevier Science Inc., USA, 2006.
  9. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Academic Press, San Diego, CA, 1998.
  10. S. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Switzerland, 1993.
  11. D.-X. Chen, Oscillatory behavior of a class of fractional differential equations with damping, U.P.B. Sci. Bull. Ser. A, 75(1) (2013), 107–118.
  12. D.-X. Chen, P.-X. Qu, Y.-H. Lan, Forced oscillation of certain fractional differential equations, Adv. Difference Equ., 2013(1) (2013), 125.
  13. Q. Feng, A. Liu, Oscillation for a class of fractional differential equation, J. Appl. Math. Phys., 7(07) (2019), 1429.
  14. S. Grace, R. Agarwal, P. Wong, A. Zafer, On the oscillation of fractional differential equations, Fract. Calc. Appl. Anal., 15(06) (2012), 222–231.
  15. Z. Han, Y. Zhao, Y. Sun, C. Zhang, Oscillation for a class of fractional differential equation Discrete Dyn. Nat. Soc., 2013 (2013).
  16. H. Qin, B. Zheng. Oscillation of a class of fractional differential equations with damping term, Sci. World J., 2013 (2013).
  17. T. Yalçın Uzun, H. Büyükçavuşoğlu Erçolak, M. K. Yıldız, Oscillation criteria for higher order fractional differential equations with mixed nonlinearities, Konuralp J. Math., 7 (2019), 203–207.
  18. J. Yang, A. Liu, T. Liu, Forced oscillation of nonlinear fractional differential equations with damping term, Adv. Difference Equ., 2015(1) (2015), 1.
  19. B. Zheng, Oscillation for a class of nonlinear fractional differential equations with damping term, J. Adv. Math. Stud., 6(1) (2013), 107–109.
  20. R. P. Agarwal, M. Bohner, T. Li, Oscillatory behavior of second-order half-linear damped dynamic equations, Appl. Math. Comput., 254 (2015), 408-418.
  21. M. Bohner, T. Li, Kamenev-type criteria for nonlinear damped dynamic equations, Sci. China Math., 58(7) (2015), 1445-1452.
  22. J. Dzurina, S. R. Grace, I. Jadlovsk´a, T. Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293(5) (2020), 910-922.
  23. T. Li, Yu. V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), Art. 106293, pp. 1-7.
  24. D. Vivek, E. Elsayed, K. Kanagarajan, On the oscillation of fractional differential equations via y-hilfer fractional derivative, Eng. Appl. Sci. Lett., 2(3) (2019), 1–6.
  25. R. P. Agarwal, M. Bohner, W.-T. Li, Nonoscillation and oscillation theory for functional differential equations, volume 267. CRC Press, 2004.
  26. R. Hilfer, P. Butzer, U. Westphal, An introduction to fractional calculus, Appl. Fract. Calc. Phys., World Scientific, (2010), 1–85.
  27. J. V. d. C. Sousa, E. C. de Oliveira, On the y-hilfer fractional derivative, Commun. Nonl. Sci. Numer. Simul., 60 (2018), 72–91.
  28. U. Katugampola, A new approach to generalized fractional derivatives, B. Math. Anal. App., 6(4) (2014), 1–15.
  29. U. Katugampola, Existence and uniqueness results for a class of generalized fractional differential equations, (2014), arXiv:1411.5229 [math.CA].