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Oscillation of impulsive conformable fractional differential equations

Jessada Tariboon, Sotiris K. Ntouyas (2016)

Open Mathematics

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,…. t k D α p t t k D α x t + r t x t + q t x t = 0 , t t 0 , t 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 , ... . Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.

Oscillation of neutral differential equations with maxima.

D. Bainov, V. Petrov, V. Proicheva (1995)

Revista Matemática de la Universidad Complutense de Madrid

In the paper ordinary neutral differential equations with ?maxima? are considered. Sufficient conditions for oscillation of all solutions are obtained.

Oscillation of second order neutral delay differential equations

J. Džurina, D. Hudáková (2009)

Mathematica Bohemica

We establish some new oscillation criteria for the second order neutral delay differential equation [ r ( t ) | [ x ( t ) + p ( t ) x [ τ ( t ) ] ] ' | α - 1 [ x ( t ) + p ( t ) x [ τ ( t ) ] ] ' ] ' + q ( t ) f ( x [ σ ( t ) ] ) = 0 . The obtained results supplement those of Dzurina and Stavroulakis, Sun and Meng, Xu and Meng, Baculíková and Lacková. We also make a slight improvement of one assumption in the paper of Xu and Meng.

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