Browsing by Author "Tunc, Ercan"

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On the Oscillation of a Class of Damped Fractional Differential Equations
(Univ Miskolc inst Math, 2016) Tunc, Ercan; Tunc, Osman
Using Riccati type transformations, the authors establish some new oscillation criteria for the fractional differential equation (D-0+(1+alpha) y) (t) + p(t) (D-0+(alpha) y) (t) + q(t) f(G(t)) = 0, t > 0, where D-0+(alpha) is the Riemann-Liouville fractional derivative of order alpha of y, G(t) = integral(t)(0) (t - s)(-alpha) y(s)ds, and alpha is an element of(0, 1). Examples are provided to illustrate the relevance of the results.
On the Asymptotic Behavior of Solutions of Certain Second-Order Differential Equations
(Pergamon-elsevier Science Ltd, 2007) Tunc, Cemil; Tunc, Ercan
In this paper, the second order non-linear differential equation (x) over dot + a(t)f (x, (x) overdot)(x) over dot+ b(t)g(x) = p(t, x, (x) over dot) is considered, and Lyapunov's second method is used to show that uniform boundedness and convergence to zero of all solutions of this equation together with their derivatives of the first order. (c) 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Instability Results for Certain Third Order Nonlinear Vector Differential Equations
(Texas State Univ, 2006) Tunc, Cemil; Tunc, Ercan
Our goal in this paper is to obtain sufficient conditions for instability of the zero solution to the non-linear vector differential equation X + F(X, (X) over dot))X + G((X) over dot) + H(X) = 0. An example illustrates the results obtained.