Billur Kaymakçalan

Lyapunov inequalities for discrete linear Hamiltonian systems

Abstract In this paper, we present some Lyapunov type inequalities for discrete linear scalar Hamiltonian systems when the coefficient c(t) is not necessarily nonnegative valued and when the end-points are not necessarily usual zeros, but rather, generalized zeros. Applying these inequalities, we obtain some disconjugacy and stability criteria for discrete Hamiltonian systems

Basics of Riemann Delta and Nabla Integration on Time Scales

In this paper we introduce and investigate the concepts of Riemanns delta and nabla integrals on time scales. Main theorems of the integral calculus on time scales are proved.

Oscillation results for a dynamic equation on a time scale

This paper is dedicated to Calvin Ahlbrandt

On coupled fixed point theorems on partially ordered G-metric spaces

In this manuscript, we extend, generalize and enrich some recent coupled fixed point theorems in the framework of partially ordered G-metric spaces in a way that is essentially more natural.MSC:46N40, 47H10, 54H25, 46T99.

The quasilinearization method for boundary value problems on time scales

Abstract In this paper, we apply the method of quasilinearization to a family of boundary value problems for second order dynamic equations − y Δ ∇ + q ( t ) y = H ( t , y ) on time scales. The results include a variety of possible cases when H is either convex or a splitting of convex and concave parts and whether lower and upper solutions are of natural form or of natural coupled form.

A new transform method in nabla discrete fractional calculus

Starting from the definition of the Sumudu transform on a general nabla time scale, we define the generalized nabla discrete Sumudu transform. We obtain the nabla discrete Sumudu transform of Taylor monomials, fractional sums, and differences. We apply this transform to solve some fractional difference equations with initial value problems.MSC:44A15, 44A55.

Nabla discrete fractional Grüss type inequality

Properties of the discrete fractional calculus in the sense of a backward difference are introduced and developed. Here, we prove a more general version of the Grüss type inequality for the nabla fractional case. An example of our main result is given.MSC: 39A12, 34A25, 26A33, 26D15, 26D20.

Behavior of the Solutions for Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on Periodic Time Scales in Shifts

We consider two-dimensional predator-prey system with Beddington-DeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system has -periodic solution.

Generalized diamond-α dynamic opial inequalities

We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opials inequality and also provide new estimates on inequalities of this type. Also, we introduce an example to illustrate our result.Mathematics Subject Classification 2000: 39A12; 26D15; 49K05