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On the nonoscillatory behavior of solutions of three classes of fractional difference equations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transfor mation technique, we employ herein an easily verifiable approach based on the fractional Taylor’s difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.
Rocznik
Strony
549--568
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
  • Faculty of Engineering, Cairo University Department of Engineering Mathematics Giza 12221, Egypt
  • Prince Sultan University Department of Mathematics and General Sciences 11586 Riyadh, Saudi Arabia
  • Periyar University Department of Mathematics Salem-636 011, Tamilnadu, India
  • Periyar University Department of Mathematics Salem-636 011, Tamilnadu, India
  • Sakarya University of Applied Sciences Vocational School of Arifiye Arifiye 54580, Sakarya, Turkey
Bibliografia
  • [1] B. Abdalla, T. Abdeljawad, On the oscil lation of Caputo fractional differential equations with Mittag-Leffler nonsingular kernel, Chaos Solitons Fract. 127 (2019), 173-177.
  • [2] B. Abdalla, K. Abodayeh, T. Abdeljawad, J. Alzabut, New oscil lation criteria for forced nonlinear fractional difference equations, Vietnam J. Math. 45 (2017), 609-618.
  • [3] B. Abdalla, J. Alzabut, T. Abdeljawad, On the oscil lation of higher order fractional difference equations with mixed nonlinearities, Hacet. J. Math. Stat. 47 (2018), 207-217.
  • [4] T. Abdeljawad, On Riemann and Caputo fractional differences, Comput. Math. Appl. 62 (2011), 1602-1611.
  • [5] J. Alzabut, T. Abdeljawad, H. Alrabaiah, Oscil lation criteria for forced and damped nabla fractional difference equations, J. Comput. Anal. Appl 24 (2018) 8, 1387-1394.
  • [6] G.A. Anastassiou, Discrete fractional calculus and inequalities, arXiv:0911.3370, (2009).
  • [7] A. Aphithana, S.K. Ntouyas, J. Tariboon, Forced oscil lation of fractional differential equations via conformable derivatives with damping term, Bound. Value Probl. 2019 (2019), 47.
  • [8] F.M. Atici, P.W. Eloe, A transform method in discrete fractional calculus, Intern. J. Difference Equ. 2 (2007), 165-176.
  • [9] F.M. Atici, P.W. Eloe, Initial value problems in discrete fractional calculus, Proc. Amer. Math. Soc. 137 (2009), 981-989.
  • [10] F.M. Atici, S. Sengul, Modeling with fractional difference equations, J. Math. Anal. Appl. 369 (2010) 1, 1-9.
  • [11] Z. Bai, R. Xu, The asymptotic behavior of solutions for a class of nonlinear fractional difference equations with damping term, Discrete Dyn. Nat. Soc. 2018 (2018).
  • [12] G.E. Chatzarakis, P. Gokulraj, T. Kalaimani, Oscil lation tests for fractional difference equations, Tatra Mt. Math. Publ. 71 (2018) 1, 53-64.
  • [13] G.E. Chatzarakis, P. Gokulraj, T. Kalaimani, V. Sadhasivam, Oscil latory solutions of nonlinear fractional difference equations, Int. J. Differ. Equ. 13 (2018), 19-31.
  • [14] F. Chen, Fixed points and asymptotic stability of nonlinear fractional difference equations, Electron. J. Qual. Theory Differ. Equ. 36 (2011), 1-18.
  • [15] D.X. Chen, Oscil lation criteria of fractional differential equations, Adv. Differ. Equ. 2012 (2012), 33.
  • [16] F. Chen, Z. Liu, Asymptotic stability results for nonlinear fractional difference equations, J. Appl. Math. 2012 (2012).
  • [17] K. Diethelm, The analysis of fractional differential equations, Springer Science & Business Media, 2010.
  • [18] C.S. Goodrich, On discrete sequential fractional boundary value problems, J. Math. Anal. Appl. 385 (2012) 1, 111-124.
  • [19] C. Goodrich, A.C. Peterson, Discrete Fractional Calculus, Springer, Berlin, 2015.
  • [20] S.R. Grace, R.P. Agarwal, P.J.Y. Wong, A. Zafer, On the oscil lation of fractional differential equations, Fract. Calc. Appl. Anal. 15 (2012), 222-231.
  • [21] S.R. Grace, A. Zafer, On the asymptotic behavior of nonoscil latory solutions of certain fractional differential equations, Eur. Phys. J. Spec. Top. 226 (2017), 3657-3665.
  • [22] G.H. Hardy, I.E. Littlewood, G. Polya, Inequalities, University Press, Cambridge, 1959.
  • [23] J.M. Holte, Discrete Gronwal l lemma and applications, [in:] Proceedings of the MAA-NCS Meeting at the University of North Dakota, (2009).
  • [24] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam, 2006.
  • [25] W.N. Li, W. Sheng, Oscil lation properties for solutions of a kind of partial fractional differential equations with damping term, J. Nonlinear Sci. Appl 9 (2016), 1600-1608.
  • [26] R.E. Mickens, Difference Equations: Theory, Applications and Advanced Topics, Taylor and Francis Group, New York, 2015.
  • [27] I. Podlubny, Fractional Differential Equations, vol. 198, Mathematics in Science and Engineering, Academic Press, San Diego, California, 1999.
  • [28] V.E. Tarasov, Frcational-order difference equations for physical lattices and some applications, J. Math. Phys. 56 (2015) 10, 1-19.
  • [29] E. Tunc, O. Tunc, On the oscil lation of a class of damped fractional differential equations, Miskolc Math. Notes 17 (2016), 647-656.
  • [30] J. Yang, A. Liu, T. Liu, Forced oscil lation of nonlinear fractional differential equations with damping term, Adv. Differ. Equ. 2015 (2015).
  • [31] Y. Zhou, A. Alsaedi, B. Ahmad, Oscil lation for fractional neutral functional differential systems, J. Comput. Anal. Appl. 25 (2018) 5, 965-974.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c655af60-5463-4612-9069-2ffa98d97e49
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