Browsing by Author "Bolat Y."

Now showing 1 - 13 of 13

Almost periodic dynamics of a discrete Nicholson's blowflies model involving a linear harvesting term Difference equations: New trends and applications in biology, medicine and biotechnology
(2012-12-01) Alzabut J.; Bolat Y.; Abdeljawad T.
We consider a discrete Nicholson's blowflies model involving a linear harvesting term. Under appropriate assumptions, sufficient conditions are established for the existence and exponential convergence of positive almost periodic solutions of this model. To expose the effectiveness of the main theorems, we support our result by a numerical example. MSC: 39A11. © 2012 Alzabut et al.; licensee Springer.
On the oscillation of even-order half-linear functional difference equations with damping term
(2014-01-01) Bolat Y.; Alzabut J.
We investigate the oscillatory behavior of solutions of the m th order half-linear functional difference equations with damping term of the form Δ [pn Q (Δm-1 yn) ] + qn Q (Δm-1 yn) + rn Q (y τ n) = 0, n ≥ n 0, where m is even and Q (s) = s α - 2 s, α > 1 is a fixed real number. Our main results are obtained via employing the generalized Riccati transformation. We provide two examples to illustrate the effectiveness of the proposed results. © 2014 Yaşar Bolat and Jehad Alzabut.
On the oscillation of fractional-order delay differential equations with constant coefficients
(2014-01-01) Bolat Y.; Bolat, Y
In this manuscript, some oscillation results are given including sufficient conditions or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions and Laplace transformation formulations of fractional-order derivatives are used. © 2014 Elsevier B.V.
On the oscillation of fractional-order delay differential equations with constant coefficients
(2014-01-01) Bolat Y.
In this manuscript, some oscillation results are given including sufficient conditions or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions and Laplace transformation formulations of fractional-order derivatives are used. © 2014 Elsevier B.V.
On the oscillation of higher-order half-linear delay difference equations
(2012-09-01) Bolat Y.; Alzabut J.
In this paper, sufficient conditions are established for the oscillatory and asymptotic behavior of higher-order half-linear delay difference equation of the form where it is assumed that ∑ s∞=n0 1/ps 1/α < ∞. The main theorem improves some existing results in the literature. An example is provided to demonstrate the effectiveness of the main result. © 2012 NSP Natural Sciences Publishing Cor.
Oscillation criteria for higher-order half-linear delay difference equations involving generalized difference operator
(2016-06-01) Bolat Y.; Akin Ö.
In this paper, oscillation criteria are obtained for higher-order half-linear delay difference equations involving generalized difference operator of the form [Equation presented here] where Δb is defined by Δbyn = yn+1 - byn, b ∈ R - {0}, p: N → R+, α, β are the ratio of odd positive integers with β ≤ α; m, n, n0, σ are non-negative integers, q: N → R. The cases of b negative and positive and qn ≥ 0, which has important role for oscillation of this equation, are considered. Also we provide some examples to illustrate our main results.
Oscillation criteria for higher-order neutral type difference equations
(2020-01-01) Köprübasi T.; ünal Z.; Bolat Y.
In this paper, oscillation criteria are obtained for higher-order neutral-type nonlinear delay difference equations of the form, where is nondecreasing; Moreover, we provide some examples to illustrate our main results.
Oscillation Criteria for Nonlinear Higher-Order Forced Functional Difference Equations
(2015-09-01) Alzabut J.; Bolat Y.
Some oscillation criteria for solutions of nonlinear higher-order forced difference equations are established. The investigations are carried out without assuming that the coefficients of the equations are of a definite sign and by showing that the forcing term needs not be the mth difference of an oscillatory function. The proposed results are supported with some examples.
OSCILLATIONS OF HIGHER-ORDER IMPULSIVE PARTIAL DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY
(2022-07-01) Bolat Y.; Chatzarakis G.E.; Panetsos S.L.; Raja T.
We consider a class of boundary value problems associated with even order nonlinear impulsive neutral partial functional differential equations with continuous distributed deviating arguments and damping term. Necessary and sufficient conditions are obtained for the oscillation of all solutions using impulsive differential inequalities and integral averaging scheme with the Robin boundary condition. Examples illustrating the results are also given
Oscillatory behaviour of a higher-order dynamic equation
(2013-12-01) Uçar D.; Bolat Y.
In this paper we are concerned with the oscillation of solutions of a certain more general higher-order nonlinear neutral-type functional dynamic equation with oscillating coefficients. We obtain some sufficient criteria for oscillatory behaviour of its solutions. © 2013 Uçar and Bolat.
Stability conditions for linear difference system with two delays
(2021-01-01) Deger S.U.; Bolat Y.
In this paper, we give new necessary and sufficient conditions for the asymptotic stability of a linear delay difference system with two delays xn+1 − axn + A (xn−k + xn−l ) = 0, n ∈ {0, 1, 2, …}, where A is a 2×2 constant matrix, a ∈ [−1, 1]−{0} is a real number and l, k are positive integers such that 1 ≤ l < k.
Stability criteria for volterra type linear nabla fractional difference equations
(2022-12-01) Gevgeşoğlu M.; Bolat Y.
In this study, we give some necessary and sufficient conditions on the stability for Volterra type linear nabla fractional difference equations of the form ∇-1vx(t)=λx(t),t∈ N1, with initial condition ∇-1v-1x(t)|t=0=x0.For this, first of all we show that the above equation is a convolution-type Volterra equation, then give the stability conditions by using the stability analysis methods of the convolution type Volterra equations. Also we give some examples to illustrate our theoretic results.
Stability criterion for volterra type delay difference equations including a generalized difference operator
(2020-01-01) Gevgesoglu M.; Bolat Y.
The stability of a class of Volterra-type difference equations that include a generalized difference operator [increment]a is investigated using Krasnoselskii's fixed point theo-rem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.