Publications

2024 (3)

Nour H.M. ALSHARIF and Basak KARPUZ*,
A test for global attractivity of linear dynamic equations with delay,
Qual. Theory Dyn. Syst., vol. 23, no. 118, pp. 1--18, (2024).
https://doi.org/10.1007/s12346-023-00907-8
Nour H.M. ALSHARIF and Basak KARPUZ*,
Some complementary results on asymptotic behavior of solutions of neutral difference equations,
Turkish J. Math., vol. 48, no. 6, pp. 1110--1126, (2024).
https://doi.org/10.55730/1300-0098.3564
Nour H.M. ALSHARIF and Basak KARPUZ*,
Yoneyama's $3/2$ test for the asymptotic stability of delay dynamic equations,
Internat. J. Control, vol. ??, no. ???, pp. ??--??, (202?).
https://doi.org/10.1080/00207179.2024.2380024

2023 (0)

2022 (1)

Basak KARPUZ* and Zehra OZSEVER,
An iterative oscillation test for delay difference equations,
Hacet. J. Math. Stat., vol. 51, no. 1, pp. 74--82, (2022).

2021 (3)

Basak KARPUZ and Halis Can KOYUNCUOĞLU*,
Positivity and uniform exponential stability for Volterra integro-dynamical systems on time scales,
Nonlinear Anal. Hybrid Syst., vol. 41, aid. 101049 , 15 p., (2021).
Basak KARPUZ* and Ioannis P. STAVROULAKIS,
Oscillation and nonoscillation of difference equations with several delays,
Mediterr. J. Math., vol. 18, no. 1, aid. 3, 15 p., (2021).
Basak KARPUZ* and Büşra ÖZSAVAŞ,
An improved product type oscillation test for partial difference equations,
Appl. Math. Comput., vol. 391, aid. 125629, 10 p., (2021).

2020 (3)

Basak KARPUZ* and Shyam S. SANTRA,
New criteria for the oscillation and asymptotic behavior of second-order neutral differential equations with several delays,
Turkish J. Math., vol. 44, no. 6, pp. 1990--2003, (2020).
Basak KARPUZ,
Sharp conditions for oscillation and nonoscillation of neutral difference equations,
Springer Proceedings in Mathematics and Statistics, vol. 312, pp. 251--265, (2020).
Elena BRAVERMAN* and Basak KARPUZ*,
Linearized oscillation theory for a nonlinear nonautonomous difference equation,
Springer Proceedings in Mathematics and Statistics, vol. 312, pp. 3--19, (2020).

2019 (3)

Basak KARPUZ* and Shyam S. SANTRA,
Oscillation theorems for second-order nonlinear delay differential equations of neutral type,
Hacet. J. Math. Stat., vol. 48, no. 3, pp. 633--643, (2019).
Basak KARPUZ,
Sharp oscillation and nonoscillation tests for delay dynamic equations,
Math. Methods Appl. Sci., vol. 42, no. 9, pp. 2993--3001, (2019).
Basak KARPUZ,
Hille—Nehari theorems for dynamic equations with a time scale independent critical constant,
Appl. Math. Comput., vol. 346, pp. 336--351, (2019).

2018 (2)

Basak KARPUZ,
Philos' inequality on time scales and its application in the oscillation theory,
Math. Inequal. Appl., vol. 21, no. 4, pp. 1029--1046, (2018).
Basak KARPUZ,
On the existence and uniqueness of solutions to dynamic equations,
Turkish J. Math., vol. 42, no. 3, pp. 1072--1089, (2018).

2017 (5)

Basak KARPUZ,
Sharp oscillation and nonoscillation tests for linear difference equations,
J. Difference Equ. Appl., vol. 23, no. 12, pp. 1929--1942, (2017).
Elena BRAVERMAN* and Basak KARPUZ,
On different types of stability for linear delay dynamic equations,
Z. Anal. Anwend., vol. 36, no. 3, pp. 343--375, (2017).
Basak KARPUZ,
Analyticity of the complex time scale exponential,
Complex Anal. Oper. Theory, vol. 11, no. 1, pp. 21--34, (2017).
Basak KARPUZ,
Sufficient conditions for the oscillation of odd-order neutral dynamic equations,
Int. J. Anal. Appl., vol. 14, no. 1, pp. 69--76, (2017).
Basak KARPUZ*, Umut M. ÖZKAN, Tuğba YALÇIN, Mustafa K. YILDIZ,
Basic theory for differential equations with unified Reimann-Liouville and Hadamard type fractional derivative,
Int. J. Anal. Appl., vol. 13, no. 2, pp. 216--230, (2017).

2016 (2)

Basak KARPUZ* and Özkan ÖCALAN,
New oscillation tests and some refinements for first-order delay dynamic equations,
Turkish J. Math., vol. 44, no. 4, pp. 850--863, (2016).
Basak KARPUZ,
Nonoscillation and oscillation of second-order linear dynamic equations via the sequence of functions technique,
J. Fixed Point Theory Appl., vol. 18, no. 4, pp. 889--903, (2016).

2015 (3)

Basak KARPUZ,
Oscillation and stability of first-order delay differential equations with retarded impulses,
Electron. J. Qual. Theory Differ. Equ., vol. 2015, no. 66, pp. 1--17, (2015).
Basak KARPUZ,
Asymptotic stability of the complex dynamic equation uΔ−z⋅u+w⋅uσ=0,
J. Math. Anal. Appl., vol. 421, no. 1, pp. 925--937, (2015).
Basak KARPUZ,
Comparison tests for the asymptotic behaviour of higher-order dynamic equations of neutral type,
Forum Math., vol. 27, no. 5, pp. 2759--2773, (2015).

2014 (4)

Basak KARPUZ,
Oscillation of solutions of linear impulsive partial difference equations with continuous variables,
Electron. J. Differential Equations, vol. 2014, no. 190, pp. 1--14, (2014).
Basak KARPUZ* and Özkan ÖCALAN,
Iterated oscillation criteria for delay partial difference equations,
Math. Bohem., vol. 139, no. 3, pp. 437--450, (2014).
Basak KARPUZ,
Necessary and sufficient conditions on the asymptotic behaviour of second-order neutral delay dynamic equations with positive and negative coefficients,
Math. Methods Appl. Sci., vol. 37, no. 8, pp. 1219--1231, (2014).
Basak KARPUZ,
Volterra theory on time scales,
Results Math., vol. 65, no. 3, pp. 263--292, (2014).

2013 (5)

Martin BOHNER*, Gusein Sh. GUSEINOV and Basak KARPUZ,
Further properties of the Laplace transform on time scales with arbitrary graininess,
Integral Transforms Spec. Funct., vol. 24, no. 4, pp. 289--301, (2013).
Martin BOHNER* and Basak KARPUZ,
The Gamma function on time scales,
Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., vol. 20, no. 4, pp. 507--522, (2013).
Basak KARPUZ,
Li type oscillation theorem for delay dynamic equations,
Math. Methods Appl. Sci., vol. 36, no. 9, pp. 993--1002, (2013).
Basak KARPUZ,
Sufficient conditions for the oscillation and asymptotic behaviour of higher-order dynamic equations of neutral type,
Appl. Math. Comput., vol. 221, pp. 453--462, (2013).
Basak KARPUZ* and Özkan ÖCALAN,
Oscillation of delay dynamic equations with oscillating coefficients,
Differ. Equ. Appl., vol. 5, no. 3, pp. 331--339, (2013).

2012 (8)

Elena BRAVERMAN* and Basak KARPUZ,
On global asymptotic stability of nonlinear higher-order difference equations,
J. Comput. Appl. Math., vol. 236, no. 11, pp. 2803--2812, (2012).
Elena BRAVERMAN* and Basak KARPUZ,
On monotonicity of nonoscillation properties of dynamic equations in time scales,
Z. Anal. Anwend., vol. 31, no. 2, pp. 203--216, (2012).
Elena BRAVERMAN* and Basak KARPUZ,
On stability of delay difference equations with variable coefficients: successive products tests,
Adv. Difference Equ., vol. 2012, aid. 177, 8 p., (2012).
Elena BRAVERMAN* and Basak KARPUZ,
Uniform exponential stability of first-order dynamic equations with several delays,
Appl. Math. Comput., vol. 218, no. 21, pp. 10468--10485, (2012).
Tuncay CANDAN, Basak KARPUZ* and Özkan ÖCALAN,
Oscillation of neutral differential equations with distributed deviating arguments,
Nonlinear Oscil. (N. Y.), vol. 15, no. 1, pp. 65--76, (2012).
Basak KARPUZ,
Oscillation of first-order differential equations with retarded arguments,
Math. Slovaca, vol. 62, no. 2, pp. 247--256, (2012).
Basak KARPUZ* and Özkan ÖCALAN,
Oscillation and nonoscillation in neutral delay dynamic equations with positive and negative coefficients,
Commun. Appl. Anal., vol. 16, no. 1, pp. 113--129, (2012).
Basak KARPUZ* and Özkan ÖCALAN,
Oscillation criteria for a class of first-order forced differential equations under impulse effects,
Adv. Dyn. Syst. Appl., vol. 7, no. 2, pp. 205--218, (2012).

2011 (10)

Martin BOHNER*, Gusein Sh. GUSEINOV and Basak KARPUZ,
Properties of the Laplace transform on time scales with arbitrary graininess,
Integral Transforms Spec. Funct., vol. 22, no. 11, 785--800, (2011).
Elena BRAVERMAN* and Basak KARPUZ,
Nonoscillation of second-order dynamic equations with several delays,
Abstr. Appl. Anal., vol. 2011, aid. 591254, 34 p., (2011).
Elena BRAVERMAN* and Basak KARPUZ,
On oscillation of differential and difference equations with non-monotone delays,
Appl. Math. Comput., vol. 218, no. 7, pp. 3880--3887, (2011).
Julio G. DIX, Basak KARPUZ* and Radhanath RATH,
Necessary and sufficient conditions for the oscillation of differential equations involving distributed arguments,
Electron. J. Qual. Theory Differ. Equ., vol. 2011, no. 19, pp. 1--15, (2011).
Lynn H. ERBE, Basak KARPUZ* and Allan C. PETERSON,
Kamenev-type oscillation criteria for higher-order neutral delay dynamic equations,
Int. J. Difference Equ., vol. 6, no. 1, pp. 1--16, (2011).
Basak KARPUZ,
Existence and uniqueness of solutions to systems of delay dynamic equations on time scales,
Int. J. Math. Comput., vol. 10, no. M11 (Special Volume), pp. 48--58, (2011).
Basak KARPUZ,
On uniqueness of the Laplace transform on time scales,
Panamer. Math. J., vol. 21, no. 2, pp. 101--110, (2011).
Basak KARPUZ,
Remarks on: “Oscillation in nonlinear neutral difference equations with positive and negative coefficients” [Int. J. Difference Equ. 5 (2010) 251--265],
Int. J. Difference Equ., vol. 6, no. 2, pp. 127--129, (2011).
Basak KARPUZ*, Özkan ÖCALAN and Sermin ÖZTÜRK,
Comparison criteria for the oscillation of mixed-type impulsive difference equations with continuous arguments,
Hacet. J. Math. Stat., vol. 40, no. 2, pp. 265--272, (2011).
Basak KARPUZ and Umut M. ÖZKAN*,
Some generalizations for Opial's inequality involving several functions and their derivatives of arbitrary order on arbitrary time scales,
Math. Inequal. Appl., vol. 14, no. 1, pp. 79--92, (2011).

2010 (8)

Elena BRAVERMAN* and Basak KARPUZ,
Nonoscillation of first-order dynamic equations with several delays,
Adv. Difference Equ., vol. 2010, aid. 873459, 22 p., (2010).
Basak KARPUZ*, Billûr KAYMAKÇALAN and Özkan ÖCALAN,
A generalization of Opial's inequality and applications to second-order dynamic equations,
Differ. Equ. Dyn. Syst. (in Memory of Bernd Aulbach), vol. 18, no. 1-2, pp. 11--18, (2010).
Basak KARPUZ, Billûr KAYMAKÇALAN and Umut M. ÖZKAN*,
Some multi-dimensional Opial-type inequalities on time scales,
J. Math. Inequal., vol. 4, no. 2, pp. 207--216, (2010).
Basak KARPUZ and Özkan ÖCALAN*,
Comparison theorems on the oscillation of a class of neutral difference equations with continuous variables,
Bull. Korean Math. Soc., vol. 47, no. 2, pp. 401--409, (2010).
Basak KARPUZ* and Özkan ÖCALAN,
Further oscillation criteria for partial difference equations with variable coefficients,
Comput. Math. Appl., vol. 59, no. 1, pp. 55--63, (2010).
Basak KARPUZ*, Özkan ÖCALAN and Sermin ÖZTÜRK,
Comparison theorems on the oscillation and asymptotic behaviour of higher-order neutral differential equations,
Glasg. Math. J., vol. 52, no. 1, pp. 107--114, (2010).
Basak KARPUZ*, Özkan ÖCALAN and Sermin ÖZTÜRK,
Oscillation of first-order impulsive difference equations with continuous arguments,
J. Comput. Anal. Appl., vol. 12, no. 2, pp. 539--543, (2010).
Basak KARPUZ*, Özkan ÖCALAN and Mustafa K. YILDIZ,
Corrigendum to “Oscillation of a class of difference equations of second order” [Math. Comput. Modelling 49 (2009) 912--917],
Math. Comput. Modelling, vol. 51, no. 9-10, pp. 1009--1010, (2010).

2009 (13)

Basak KARPUZ,
Asymptotic behaviour of bounded solutions of a class of higher-order neutral dynamic equations,
Appl. Math. Comput., vol. 215, no. 6, pp. 2174--2183, (2009).
Basak KARPUZ,
Remarks on: “Oscillation criteria for second-order functional difference equation with neutral terms” [Demon. Math. 41 (2008) 615--625],
Demonstratio Math., vol. 52, no. 3, pp. 549--551, (2009).
Basak KARPUZ,
Some oscillation and nonoscillation criteria for neutral delay difference equations with positive and negative coefficients,
Comput. Math. Appl., vol. 57, no. 4, pp. 633--642, (2009).
Basak KARPUZ,
Unbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients,
Electron. J. Qual. Theory Differ. Equ., vol. 2009, no. 34, pp. 1--14, (2009).
Basak KARPUZ*, Jelena V. MANOJLOVIC, Özkan ÖCALAN and Yutaka SHOUKAKU,
Oscillation criteria for a class of second-order neutral delay differential equations,
Appl. Math. Comput., vol. 210, no. 2, pp. 303--312, (2009).
Basak KARPUZ* and Özkan ÖCALAN,
Necessary and sufficient conditions on asymptotic behaviour of solutions of forced neutral delay dynamic equations,
Nonlinear Anal., vol. 71, no. 7-8, pp. 3063--3071, (2009).
Basak KARPUZ* and Özkan ÖCALAN,
Oscillation and nonoscillation of first-order dynamic equations with positive and negative coefficients,
Dynam. Systems Appl., vol. 18, no. 3-4, pp. 363--374, (2009).
Basak KARPUZ*, Özkan ÖCALAN and Radhanath RATH,
Necessary and sufficient conditions for the oscillatory and asymptotic behaviour of solutions to neutral delay dynamic equations,
Electron. J. Differential Equations, vol. 2009, no. 64, pp. 1--15, (2009).
Basak KARPUZ*, Özkan ÖCALAN and Mustafa K. YILDIZ,
Oscillation of a class of difference equations of second order,
Math. Comput. Modelling, vol. 49, no. 5-6, pp. 912--917, (2009).
Basak KARPUZ*, Özkan ÖCALAN and Mustafa K. YILDIZ,
Oscillation of higher-order nonlinear delay differential equations with oscillatory coefficients,
Turkish J. Math., vol. 33, no. 3, pp. 259--263, (2009).
Basak KARPUZ, Radhanath RATH* and Subhendu K. RATH,
On oscillation and asymptotic behaviour of a higher order functional difference equation of neutral type,
Int. J. Difference Equ., vol. 4, no. 1, pp. 69--96, (2009).
Basak KARPUZ and Hüseyin YILDIRIM*,
A method on the general solution of inhomogeneous Euler differential equations,
Selçuk J. Appl. Math., vol. 10, no. 1, pp. 19--32, (2009).
Mustafa K. YILDIZ*, Basak KARPUZ and Özkan ÖCALAN,
Oscillation of nonlinear neutral delay differential equations of second-order with positive and negative coefficients,
Turkish J. Math., vol. 33, no. 4, pp. 341--350, (2009).

2008 (8)

Martin BOHNER, Basak KARPUZ* and Özkan ÖCALAN,
Iterated oscillation criteria for delay dynamic equations of first-order,
Adv. Difference Equ., vol. 2008, aid. 458687, 12 p., (2008).
Basak KARPUZ* and Özkan ÖCALAN,
Discrete approach on oscillation of difference equations with continuous variable,
Adv. Dyn. Syst. Appl., vol. 3, no. 2, pp. 283--290, (2008).
Basak KARPUZ* and Özkan ÖCALAN,
Erratum to: “Oscillation of forced neutral differential equations with positive and negative coefficients” [Comput. Math. Appl. 54 (2007) 1411--1421],
Comput. Math. Appl., vol. 56, no. 2, pp. 590--591, (2008).
Basak KARPUZ* and Özkan ÖCALAN,
Erratum to: “Stability for first-order delay dynamic equations on time scales” [Comput. Math. Appl. 53 (2007) 1820--1831],
Comput. Math. Appl., vol. 56, no. 4, pp. 1157--1158, (2008).
Basak KARPUZ* and Özkan ÖCALAN,
Oscillation criteria for some classes of linear delay differential equations of first-order,
Bull. Inst. Math. Acad. Sin. (N.S.), vol. 3, no. 2, pp. 293--314, (2008).
Basak KARPUZ* and Umut M. ÖZKAN,
Generalized Ostrowski's inequality on time scales,
JIPAM. J. Inequal. Pure Appl. Math., vol. 9, no. 4, aid. 112, 7 p., (2008).
Basak KARPUZ, Laxmi N. PADHY and Radhanath RATH*,
Oscillation and asymptotic behaviour of a higher order neutral differential equation with positive and negative coefficients,
Electron. J. Differential Equations, vol. 2008, no. 113, pp. 1--15, (2008).
Özkan ÖCALAN*, Mustafa K. YILDIZ and Basak KARPUZ,
On the oscillation of nonlinear neutral differential equation with positive and negative coefficients,
Dynam. Systems Appl., vol. 17, pp. 667--675, (2008).

2007 (1)

Basak KARPUZ*, Özkan ÖCALAN and Umut M. ÖZKAN,
Comparison theorems on oscillatory nature of higher order difference equations with continuous variables,
International Journal: Mathematical Manuscripts, vol. 1, no. 1, pp. 73--81, (2007).