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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: 10Citation - Scopus: 12Further Properties of the Laplace Transform on Time Scales With Arbitrary Graininess(Taylor & Francis Ltd, 2013) Bohner, Martin; Guseinov, Gusein Sh; Karpuz, BasakIn 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.Article Citation - WoS: 27Citation - Scopus: 39Properties of the Laplace transform on time scales with arbitrary graininess(Taylor & Francis Ltd, 2011) Bohner, Martin; Guseinov, Gusein Sh.; Karpuz, BasakWe 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.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.
