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Citation - WoS: 77
Citation - Scopus: 85
Double 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.
Citation - WoS: 12
Citation - Scopus: 16
The 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.