Browsing by Author "Tunç, Ercan"

Now showing 1 - 4 of 4

Access status: Open Access ,
Novel oscillation criteria for third-order semi-canonical differential equations with an advanced neutral term
(Wydawnictwa AGH, 2025) Vidhyaa, Kumar S.; Thandapani, Ethiraju; Tunç, Ercan
The main purpose of this paper is to present new oscillation results for nonlinear semi-canonical third-order differential equations with an advanced neutral term. The main idea is first by reducing the studied semi-canonical equation into standard canonical type equation without assuming any extra conditions. Then, by using the comparison method and integral averaging technique, sufficient conditions are established to ensure the oscillation of the reduced canonical equation, which in turn leads to the oscillation of the original equation. Therefore, the technique used here is very useful since the results already known for the canonical equations can be applied to obtain the oscillation of the semi-canonical equations. Two examples are provided to illustrate the importance of the main results
Access status: Open Access ,
On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
(Wydawnictwa AGH, 2020) Graef, John R.; Grace, Said R.; Tunç, Ercan
This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form $^{C}D_{c}^{\alpha}y(t)+f(t,x(t))=e(t)+k(t)x^{\eta}(t)+h(t,x(t)),$ where $t\geq c \geq 1$, $\alpha \in (0,1)$, $\eta \geq 1$ is the ratio of positive odd integers, and $^{C}D_{c}^{\alpha}y$ denotes the Caputo fractional derivative of $y$ of order $\alpha$. The cases $y(t)=(a(t)(x^{\prime}(t))^{\eta})^{\prime} \quad \text{and} \quad y(t)=a(t)(x^{\prime}(t))^{\eta}$ are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
Access status: Open Access ,
Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term
(Wydawnictwa AGH, 2019) Graef, John R.; Grace, Said R.; Tunç, Ercan
The authors present a new technique for the linearization of even-order nonlinear differential equations with a sublinear neutral term. They establish some new oscillation criteria via comparison with higher-order linear delay differential inequalities as well as with first-order linear delay differential equations whose oscillatory characters are known. Examples are provided to illustrate the theorems.
Access status: Open Access ,
Oscillatory behavior of second-order damped differential equations with a superlinear neutral term
(Wydawnictwa AGH, 2020) Tunç, Ercan; Özdemir, Osman
This article concerns the oscillatory behavior of solutions to second-order damped nonlinear differential equations with a superlinear neutral term. The results are obtained by a Riccati type transformation as well as by an integral criterion. Examples illustrating the results are provided and some suggestions for further research are indicated.