Browsing by Author "Kaymakçalan, Billur"

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Extensions of Diamond Alpha Hardy-Copson Type Dynamic İnequalities and Their Applications to Oscillation Theory
(2021) Kayar, Zeynep; Kaymakçalan, Billur
This paper is devoted to 0 < ζ < 1 complements of the classical (ζ > 1) diamond alpha Hardy-Copson type dynamic inequalities and their applications to dynamic equations. We obtain two kinds of diamond alpha Hardy-Copson type inequalities for 0 < ζ < 1, one of which is mixed type and established by the convex linear combinations of delta and nabla integrals while the other one is obtained by a new method which uses time scale calculus rather than algebra. In addition to their novelty, these two types are the complements of the classical diamond alpha Hardy-Copson type inequalities. In contrast to the works existing in the literature, these complements are derived by preserving the directions of the classical inequalities. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities obtained for 0 < ζ < 1 into one diamond alpha Hardy-Copson type inequalities and offer new types of diamond alpha Hardy-Copson type inequalities which have the same directions as the classical ones and can be considered as complementary to such inequalities. Moreover the application of these inequalities in the oscillation theory of half linear dynamic equations provides several nonoscillation criteria for such equations.
Oscillation criteria for even order dynamic equations on time-scales
(2011) Grace, Said R.; Agarwal, Ravi P.; Kaymakçalan, Billur
Some new criteria for the oscillation of even order linear dynamic equations on time-scales of the form xΔn(t) + q(t)x(t) = 0 are established.
Quantum calculus with the notion δ±-periodicity and its applications
(2018) Pelen, Neslihan Nesliye; Güvenilir, Ayşe Feza; Kaymakçalan, Billur
The relation between the time scale calculus and quantum calculus and the δ ± -periodicity in quantum calculus with the notion is considered. As an application, in two-dimensional predator–prey system with Beddington-DeAngelis-type functional response on periodic time scales in shifts is used.
Citation - WoS: 1
Some Results on Predator-Prey Dynamic Systems With Beddington-Deangelis Type Functional Response on Time Scale Calculus
(Dynamic Publishers, inc, 2017) Kaymakçalan, Billur; Pelen, Neslihan Nesliye; Guvenilir, Ayse Feza; Kaymakcalan, Billur; Matematik
We consider two dimensional predator-prey system with Beddington-DeAngelis type functional response on time scales. For this special case, we try to find under which conditions the system is permanent and globally attractive. This study gives beneficial results for continuous and discrete cases and also for solving open problems related to the dynamical properties of the systems which include the species that have unusual life cycle.