Browsing by Author "Bohner, Martin"

Now showing 1 - 10 of 10

Citation - WoS: 45
Citation - Scopus: 61
The Convolution on Time Scales
(Hindawi Publishing Corporation, 2007) Bohner, Martin; Guseinov, Gusein Sh.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. Via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. As an extensive example, we consider the q-difference equations case. Copyright (c) 2007 M. Bohner and G. Sh. Guseinov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citation - WoS: 77
Citation - Scopus: 85
Double Integral Calculus of Variations on Time Scales
(Pergamon-elsevier Science Ltd, 2007) Bohner, Martin; Guseinov, Gusein Sh.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler-Lagrange equation. (C) 2007 Elsevier Ltd. All rights reserved.
Citation - WoS: 9
Citation - Scopus: 11
Further Properties of the Laplace Transform on Time Scales With Arbitrary Graininess
(Taylor & Francis Ltd, 2013) Bohner, Martin; Guseinov, Gusein Sh; Karpuz, Basak; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this work, we generalize several properties of the usual Laplace transform to the Laplace transform on arbitrary time scales. Among them are translation theorems, transforms of periodic functions, integration of transforms, transforms of derivatives and integrals, and asymptotic values.
Citation - WoS: 53
Citation - Scopus: 67
The h-laplace and q-laplace Transforms
(Academic Press inc Elsevier Science, 2010) Bohner, Martin; Guseinov, Gusein Sh.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the particular concepts of the h-Laplace and q-Laplace transforms. The convolution and inversion problems for these transforms are considered in some detail. (c) 2009 Elsevier Inc. All rights reserved.
Citation - WoS: 4
An Introduction To Complex Functions on Products of Two Time Scales
(Taylor & Francis Ltd, 2006) Bohner, Martin; Guseinov, Gusein SH.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we study the concept of analyticity for complex-valued functions of a complex time scale variable, derive a time scale counter-part of the classical Cauchy-Riemann equations, introduce complex line delta and nabla integrals along time scales curves, and obtain a time scale version of the classical Cauchy integral theorem.
Citation - WoS: 11
Citation - Scopus: 15
The Laplace Transform on Isolated Time Scales
(Pergamon-elsevier Science Ltd, 2010) Bohner, Martin; Guseinov, Gusein Sh.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classical theorem of Titchmarsh for the usual continuous convolution. (C) 2010 Elsevier Ltd. All rights reserved.
Citation - WoS: 19
Citation - Scopus: 20
Line Integrals and Green's Formula on Time Scales
(Academic Press inc Elsevier Science, 2007) Bohner, Martin; Guseinov, Gusein Sh.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper we study curves parametrized by a time scale parameter, introduce line delta and nabla integrals along time scale curves, and obtain an analog of Green's formula in the time scale setting. (c) 2006 Elsevier Inc. All rights reserved.
Citation - WoS: 15
Multiple Lebesgue Integration on Time Scales
(Hindawi Publishing Corporation, 2006) Bohner, Martin; Guseinov, Gusein Sh.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated. Copyright (c) 2006 M. Bohner and G. Sh. Guseinov.
Citation - WoS: 25
Citation - Scopus: 36
Properties of the Laplace transform on time scales with arbitrary graininess
(Taylor & Francis Ltd, 2011) Bohner, Martin; Guseinov, Gusein Sh.; Karpuz, Basak; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We generalize several standard properties of the usual Laplace transform to the Laplace transform on arbitrary time scales. Some of these properties were justified earlier under certain restrictions on the graininess of the time scale. In this work, we have no restrictions on the graininess.
Citation - WoS: 6
Citation - Scopus: 7
Surface Areas and Surface Integrals on Time Scales
(Dynamic Publishers, inc, 2010) Bohner, Martin; Guseinov, Gusein Sh; Mathematics; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We study surfaces parametrized by time scale parameters, obtain an integral fomula for computing the area of time scale surfaces, introduce delta integrals over time scale surfaces, and give sufficient conditions that ensure existence of these integrals