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In this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form tkDαpttkDαxt+rtxt+qtxt=0,t≥t0,t≠tk,xtk+=akx(tk−),tkDαxtk+=bktk−1Dαx(tk−),k=1,2,…. $\{\begin{matrix} t_{k} D^{α} (p (t) [t_{k} D^{α} x (t) + r (t) x (t)]) + q (t) x (t) = 0, t \geq t_{0}, t \neq t_{k}, \\ x (t_{k}^{+}) = a_{k} x (t_{k}^{-}), t_{k} D^{α} x (t_{k}^{+}) = b_{k t_{k - 1}} D^{α} x (t_{k}^{-}), k = 1, 2, ... . \end{matrix}$ Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.

Oscillation of solutions of a non-linear delay differential equation of the fourth order

Pavol Šoltés (1978)

Archivum Mathematicum

Oscillation of solutions to impulsive dynamic equations on time scales.

Li, Qiaoluan, Guo, Fang (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of the solutions of a class of impulsive differential equations with a deviating argument.

Bainov, D.D., Dimitrova, Margarita B., Dishliev, Angel B. (1998)

Journal of Applied Mathematics and Stochastic Analysis

Oscillation theorems for certain nonlinear differential equations with deviating arguments

Said R. Grace, Bikkar S. Lalli (1986)

Czechoslovak Mathematical Journal

Oscillation theorems for nonlinear second order differential equations with a damping term

Said R. Grace, Bikkar S. Lalli (1989)

Commentationes Mathematicae Universitatis Carolinae

Oscillation theorems for second order nonlinear delay inequalities

Ján Seman (1989)

Mathematica Slovaca

Oscillation theorems for third order nonlinear differential equations

Anton Škerlík (1992)

Mathematica Slovaca

Oscillations of all solutions of functional differential inequalities

Jarosław Werbowski (1986)

Czechoslovak Mathematical Journal

Oscillatory and asymptotic properties of third and fourth order linear differential equations

Ján Ohriska (1989)

Czechoslovak Mathematical Journal

Oscillatory and nonoscillatory solutions for first order impulsive differential inclusions

Mouffak Benchohra, Abdelghani Ouahab (2005)

Commentationes Mathematicae Universitatis Carolinae

In this paper we discuss the existence of oscillatory and nonoscillatory solutions of first order impulsive differential inclusions. We shall rely on a fixed point theorem of Bohnenblust-Karlin combined with lower and upper solutions method.

Oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales

Mouffak Benchohra, Samira Hamani, Johnny Henderson (2007)

Archivum Mathematicum

In this paper we discuss the existence of oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales. We shall rely of the nonlinear alternative of Leray-Schauder type combined with lower and upper solutions method.

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