A NOTE ON ASYMPTOTIC BEHAVIOR OF FRACTIONAL DIFFERENTIAL EQUATIONS

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

Hakan Adıgüzel

Öz

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

Anahtar Kelimeler

Nonoscillation, fractional derivative, asymptotic behavior

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.