THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

OSCILLATION THEOREMS FOR CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONS WITH DAMPING

ABSTRACT
In this study, we study the oscillatory solutions of conformable fractional differential equations with damping term. Some examples have been given to illustrate the results.
KEYWORDS
PAPER SUBMITTED: 2022-07-12
PAPER REVISED: 2022-08-10
PAPER ACCEPTED: 2022-09-25
PUBLISHED ONLINE: 2023-01-29
DOI REFERENCE: https://doi.org/10.2298/TSCI22S2695C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 2, PAGES [695 - 702]
REFERENCES
  1. Glöckle, W. G., Nonnenmacher, T. F., A Fractional Calculus Approach to Self-Similar Protein Dynamics, Biophysical Journal, 68 (1995), 1, pp 46-53
  2. Mainardi, F., Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, Vienna, 1997, pp. 291-348
  3. Metzler, R., et al., Relaxation in Filled Polymers: A Fractional Calculus Approach, The Journal of Chemical Physics, 103 (1995), 16, pp. 7180-7186
  4. Diethelm, K., The Analysis of Fractional Differential, Springer, Berlin, Germany, 2010
  5. Podlubny I., Fractional Differential Equations, Academic, San Diego, Cal., USA, 1999
  6. Khalil, R., et al., A New Defnition of Fractional Derivative, Journal of Computational and Applied Mathematics, 264 (2014), July, pp. 65-70
  7. Abdeljawad, T., On Conformable Fractional Calculus, Journal of Computational and Applied Mathematics, 279 (2015), May, pp. 57-66
  8. Lazo, M. J., Torres, D. F., Variational Calculus with Conformable Fractional Derivatives, IEEE/CAA Journal of Automatica Sinica, 4 (2017), 2, pp. 340-352
  9. Atangana, A., et al., New Properties of Conformable Derivative, Open Mathematics, 13 (2015), 1, pp. 889-898
  10. Zhao, D., Luo, M., General Conformable Fractional Derivative and Its Physical Interpretation, Calcolo, 54 (2017), 3, pp. 903-917
  11. Abdullah, H. K., A Note on the Oscillation of Second Order Differential Equations, Czechoslovak Mathematical Journal, 54 (2004), 4, pp. 949-954
  12. Tunc, E., Tunc, O., On the Oscillation of a Class of Damped Fractional Differential Equations, Miskolc Mathematical Notes, 17 (2016), 1, pp. 647-656
  13. Ogrekci, S., et al., On the Oscillation of a Second-Order Non-linear Differential Equations With Damping, Miskolc Mathematical Notes, 18 (2017), 1, pp. 365-378
  14. Ogrekci, S., New Interval Oscillation Criteria for Second-Order Functional Differential Equations with Non-linear Damping, Open Mathematics, 13 (2015), 1, pp. 239-246
  15. Bolat, Y., On the Oscillation of Fractional-Order Delay Differential Equations with Constant Coefficients, Communications in Non-linear Science and Numerical Simulation, 19 (2014), 11, pp. 3988-3993
  16. Chen, D.-X., Oscillation Criteria of Fractional Differential Equations, Advances in Difference Equations, 2012 (2012), 33, pp. 1-10
  17. Adiguzel, H., A Note on Asymptotic Behavior of Fractional Differential Equations, Sigma Journal of Engineering and Natural Sciences, 38 (2020), 2, pp. 1061-1067
  18. Abdalla, B., et al., On the Oscillation of Higher Order Fractional Difference Equations with Mixed Non-linearities, Hacettepe Journal of Mathematics and Statistics, 47 (2018), 2, pp. 207-217
  19. Bayram, M., et al., Oscillatory Behavior of Solutions of Differential Equations with Fractional Order, Applied Mathematics & Information Sciences. Appl. Math. Inf. Sci., 11 (2017), 3, pp. 683-691
  20. Agarwal, R. P., et al., Oscillation Theory for Second Order Linear, Half Linear, Super Linear and Sub Linear Dynamic Equations, Kluwer Academic Publishers, Boston, Mass., USA, 2002
  21. Agarwal, R. P., et al., Non-oscillation and Oscillation: Theory for Functional Differential Equations, Marcel Dekker Inc., New York, USA, 2004
  22. Grace, S. R., et al., Asymptotic Behavior of Positive Solutions for Three Types of Fractional Difference Equations with Forcing Term, Vietnam Journal of Mathematics, 49 (2021), 4, pp. 1151-1164
  23. Alzabut, J., et al., On the Oscillation of Non-Linear Fractional Difference Equations with Damping, Mathematics, 7 (2019), 8, 687
  24. Muthulakshmi, V., Pavithra, S., Oscillatory Behavior Of Fractional Differential Equation with Damping, 5 (2017), 4C, pp. 383-388
  25. Bayram, M., et al., On the Oscillation of Fractional Order Non-linear Differential Equations, Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21 (2017), 6, pp. 1512-1523
  26. Shao, J., Zheng, Z., Kamenev Type Oscillatory Criteria for Linear Conformable Fractional Differential Equations, Discrete Dynamics in Nature and Society, 2019 (2019), 2310185
  27. Adiguzel, H., On the Oscillatory Behaviour of Solutions of Non-Linear Conformable Fractional Differential Equations, New Trends in Mathematical Sciences, 7 (2019), 3, pp. 379-386
  28. Bayram, M., Secer, A., Some Oscillation Criteria for Non-Linear Conformable Fractional Differential Equations, Journal of Abstract and Computational Mathematics, 5 (2010), 1, pp. 10-16

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence