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Article Citation - WoS: 12Citation - Scopus: 16The Laplace Transform on Isolated Time Scales(Pergamon-elsevier Science Ltd, 2010) Bohner, Martin; Guseinov, Gusein Sh.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.Article Citation - WoS: 55Citation - Scopus: 68The h-laplace and q-laplace Transforms(Academic Press inc Elsevier Science, 2010) Bohner, Martin; Guseinov, Gusein Sh.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.Article Citation - WoS: 77Citation - Scopus: 85Double Integral Calculus of Variations on Time Scales(Pergamon-elsevier Science Ltd, 2007) Bohner, Martin; Guseinov, Gusein Sh.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.Article Citation - WoS: 21Citation - Scopus: 22Line Integrals and Green's Formula on Time Scales(Academic Press inc Elsevier Science, 2007) Bohner, Martin; Guseinov, Gusein Sh.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.
