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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: 1Citation - Scopus: 2Existence of Solutions for Odd-Order Multi-Point Impulsive Boundary Value Problems on Time Scales(Walter de Gruyter Gmbh, 2022) Georgiev, Svetlin G.; Akgol, Sibel Dogru; Kus, Murat EymenUsing a fixed point theorem due to Schaefer, the existence of solutions for an odd-order m-point impulsive boundary value problem on time scales is obtained. The problem considered is of general form, where both the differential equation and the impulse effects are nonlinear. Illustrative examples are provided.Article Citation - WoS: 52Citation - Scopus: 62Basics of Riemann Delta and Nabla Integration on Time Scales(Taylor & Francis Ltd, 2002) Guseinov, GS; Kaymakçalan, BIn this paper we introduce and investigate the concepts of Riemann's delta and nabla integrals on time scales. Main theorems of the integral calculus on time scales are proved.Article Citation - WoS: 2Citation - Scopus: 2A Normal Distribution on Time Scales With Application(Univ Nis, Fac Sci Math, 2022) Aksoy, Umit; Cuchta, Tom; Georgiev, Svetlin; Okur, Yeliz YolcuWe introduce a new normal distribution on time scales. Based on this generalized normal distribution, a Brownian motion is introduced and its quadratic variation is derived.Article Citation - WoS: 4Citation - Scopus: 4Existence of Positive Solutions of a Sturm-Liouville Bvp on an Unbounded Time Scale(Taylor & Francis Ltd, 2008) Topal, S. Gulsan; Yantir, Ahmet; Cetin, ErbilA fixed point theorem of Guo-Krasnoselskii type is used to establish existence results for the nonlinear Sturm-Liouville dynamic equation (p(t)x(Delta))(del) + lambda phi(t)f(t,x(t)) = 0 with the boundary conditions on an unbounded time scale. Later on the positivity and the boundedness of the solutions are obtained by imposing some conditions on f.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.Article Citation - WoS: 1Citation - Scopus: 1On a system of second-order multi-point boundary value problems on time scales(Tbilisi Centre Math Sci, 2021) Oguz, Arzu Denk; Topal, S. GulsanThis paper is concerned with the existence and nonexistence of positive solutions for a system of nonlinear second order dynamic equations with multi-point boundary conditions on time scales.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: 33Citation - Scopus: 46Higher-Order Self-Adjoint Boundary-Value Problems on Time Scales(Elsevier Science Bv, 2006) Anderson, Douglas R.; Guseinov, Gusein Sh.; Hoffacker, JoanIn this study, higher-order self-adjoint differential expressions on time scales and their associated self-adjoint boundary conditions are discussed. The symmetry property of the corresponding Green's functions is shown, together with specific formulas of Green's functions for select time scales. (c) 2005 Elsevier B.V. All rights reserved.
