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A NOTE ON ASYMPTOTIC BEHAVIOR OF FRACTIONAL DIFFERENTIAL EQUATIONS

Yıl 2020, Cilt: 38 Sayı: 2, 1061 - 1067, 01.06.2021

Öz

The purpose of the study is to present some new criteria for the asymptotic behavior of nonlinear fractional differential equations.

Kaynakça

  • [1] Hilfer, R., (2000), Applications of Fractional Calculus in Physics, World Scientific, Singapore.
  • [2] Podlubbny, I., (1999), Fractional Differential Equations, Academic Press, San Diego.
  • [3] Diethelm, K., (2010), The Analysis of Fractional Differential Equations, Springer, Berlin.
  • [4] Hammet, M. E., (1971), Nonoscillation Properties of a Nonlinear Differential Equation, Proceedings of the American Mathematical Society 30,1,92-96.
  • [5] Grace, S. R., Lalli, B. S., (1988), Oscillations in second order differential equations with alternating coefficients, Periodica Mathematica Hungarica 19,1, 69-78.
  • [6] Tiryaki, A., (2012), Some criteria for the asymptotic behavior of a certain second order nonlinear perturbed differential equation, Advances in Pure Mathematics 2,5, 341-343.
  • [7] Grace, S. R., (1991), Oscillatory and asymptotic behavior of certain functional differential equations, Journal of Mathematical Analysis and Applications 62, 1, 177-188.
  • [8] Tunç C., (2007), On the non-oscillation of solutions of some nonlinear differential equations of third order, Nonlinear Dynamics and Systems Theory 7,4, 419–430.
  • [9] Agarwal, R. P., Grace S. R., Regan, D. O., (2003), oscillation theory for second order dynamic equations, Taylor and Francis, London.
  • [10] Philos, Ch. G., (1981), On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays, Archiv der Mathematik, 36, 1, 168-170.
  • [11] Mısır, A., Öğrekçi, S., (2016), Oscillation criteria for a class of second order nonlinear differential equations, Gazi University Journal of Science, 29,4,923-927.
  • [12] Agarwal, R. P., Grace, S. R., Manojlovic, J. V., (2006), Oscillation criteria for certain fourth order nonlinear functional differential equations, Mathematical and computer modelling 44,1- 2,163-187.
  • [13] Mısır, A., Öğrekçi, S., (2016), Oscillation Theorems for Second-Order Nonlinear Differential Equations, Gazi University Journal of Science 29,4,929-935.
  • [14] Tunç, E., Tunç, O., (2016), On the oscillation of a class of damped fractional differential equations, Miskolc Mathematical Notes, 17,1,647-656.
  • [15] Muthulakshmi, V., Pavithra, S., (2017), Oscillatory behavior of fractional differential equation with damping, International Journal of Mathematics And its Applications 5, 4C, 383-388.
  • [16] Chen, D., Qu, P., Lan, Y., (2013), Forced oscillation of certain fractional differential equations, Adv. Differ. Equ. Article ID 125.
  • [17] Bolat, Y., (2014), On the oscillation of fractional-order delay differential equations with constant coefficients, Communications in Nonlinear Science and Numerical Simulation, 19,11,3988-3993.
  • [18] Chen, D., (2012), Oscillation criteria of fractional differential equations, Adv. Differ. Equ. Article ID 33
  • [19] Grace, SR., Agarwal, RP., Wong, JY., Zafer, A., (2012), On the oscillation of fractional differential equations, Fract. Calc. Appl. Anal. 15: 222-231.
  • [20] Zheng, B., (2013), Oscillation for a class of nonlinear fractional differential equations with damping term, J. Adv. Math. Stud. 6, 107-115.
  • [21] Kısalar, S., Yıldız, M. K., Aktoprak, E., (2015), Oscillation of higher order fractional nonlinear difference equations, International Journal of Difference Equations, 10,2, 201-212.
  • [22] Abdalla, B., Abodayeh, K., Abdeljawad, T., Alzabut, J.,(2017), New oscillation criteria for forced nonlinear fractional difference equations, Vietnam Journal of Mathematics 45,4,609-618.
  • [23] Alzabut, J. O., Abdeljawad, T., (2014), Sufficient conditions for the oscillation of nonlinear fractional difference equations, J. Fract. Calc. Appl, 5,1, 177-187.
Yıl 2020, Cilt: 38 Sayı: 2, 1061 - 1067, 01.06.2021

Öz

Kaynakça

  • [1] Hilfer, R., (2000), Applications of Fractional Calculus in Physics, World Scientific, Singapore.
  • [2] Podlubbny, I., (1999), Fractional Differential Equations, Academic Press, San Diego.
  • [3] Diethelm, K., (2010), The Analysis of Fractional Differential Equations, Springer, Berlin.
  • [4] Hammet, M. E., (1971), Nonoscillation Properties of a Nonlinear Differential Equation, Proceedings of the American Mathematical Society 30,1,92-96.
  • [5] Grace, S. R., Lalli, B. S., (1988), Oscillations in second order differential equations with alternating coefficients, Periodica Mathematica Hungarica 19,1, 69-78.
  • [6] Tiryaki, A., (2012), Some criteria for the asymptotic behavior of a certain second order nonlinear perturbed differential equation, Advances in Pure Mathematics 2,5, 341-343.
  • [7] Grace, S. R., (1991), Oscillatory and asymptotic behavior of certain functional differential equations, Journal of Mathematical Analysis and Applications 62, 1, 177-188.
  • [8] Tunç C., (2007), On the non-oscillation of solutions of some nonlinear differential equations of third order, Nonlinear Dynamics and Systems Theory 7,4, 419–430.
  • [9] Agarwal, R. P., Grace S. R., Regan, D. O., (2003), oscillation theory for second order dynamic equations, Taylor and Francis, London.
  • [10] Philos, Ch. G., (1981), On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays, Archiv der Mathematik, 36, 1, 168-170.
  • [11] Mısır, A., Öğrekçi, S., (2016), Oscillation criteria for a class of second order nonlinear differential equations, Gazi University Journal of Science, 29,4,923-927.
  • [12] Agarwal, R. P., Grace, S. R., Manojlovic, J. V., (2006), Oscillation criteria for certain fourth order nonlinear functional differential equations, Mathematical and computer modelling 44,1- 2,163-187.
  • [13] Mısır, A., Öğrekçi, S., (2016), Oscillation Theorems for Second-Order Nonlinear Differential Equations, Gazi University Journal of Science 29,4,929-935.
  • [14] Tunç, E., Tunç, O., (2016), On the oscillation of a class of damped fractional differential equations, Miskolc Mathematical Notes, 17,1,647-656.
  • [15] Muthulakshmi, V., Pavithra, S., (2017), Oscillatory behavior of fractional differential equation with damping, International Journal of Mathematics And its Applications 5, 4C, 383-388.
  • [16] Chen, D., Qu, P., Lan, Y., (2013), Forced oscillation of certain fractional differential equations, Adv. Differ. Equ. Article ID 125.
  • [17] Bolat, Y., (2014), On the oscillation of fractional-order delay differential equations with constant coefficients, Communications in Nonlinear Science and Numerical Simulation, 19,11,3988-3993.
  • [18] Chen, D., (2012), Oscillation criteria of fractional differential equations, Adv. Differ. Equ. Article ID 33
  • [19] Grace, SR., Agarwal, RP., Wong, JY., Zafer, A., (2012), On the oscillation of fractional differential equations, Fract. Calc. Appl. Anal. 15: 222-231.
  • [20] Zheng, B., (2013), Oscillation for a class of nonlinear fractional differential equations with damping term, J. Adv. Math. Stud. 6, 107-115.
  • [21] Kısalar, S., Yıldız, M. K., Aktoprak, E., (2015), Oscillation of higher order fractional nonlinear difference equations, International Journal of Difference Equations, 10,2, 201-212.
  • [22] Abdalla, B., Abodayeh, K., Abdeljawad, T., Alzabut, J.,(2017), New oscillation criteria for forced nonlinear fractional difference equations, Vietnam Journal of Mathematics 45,4,609-618.
  • [23] Alzabut, J. O., Abdeljawad, T., (2014), Sufficient conditions for the oscillation of nonlinear fractional difference equations, J. Fract. Calc. Appl, 5,1, 177-187.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Research Articles
Yazarlar

Hakan Adıgüzel Bu kişi benim 0000-0002-8948-806X

Yayımlanma Tarihi 1 Haziran 2021
Gönderilme Tarihi 3 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 38 Sayı: 2

Kaynak Göster

Vancouver Adıgüzel H. A NOTE ON ASYMPTOTIC BEHAVIOR OF FRACTIONAL DIFFERENTIAL EQUATIONS. SIGMA. 2021;38(2):1061-7.

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