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Conference Object On the Riemann Integration on Time Scales(Crc Press-taylor & Francis Group, 2004) 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: 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: 4An Introduction To Complex Functions on Products of Two Time Scales(Taylor & Francis Ltd, 2006) Bohner, Martin; Guseinov, Gusein SH.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.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: 52Citation - Scopus: 61Basics 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: 281Citation - Scopus: 309Integration on Time Scales(Academic Press inc Elsevier Science, 2003) Guseinov, GS; Hüseyin, Hüseyin Şirin; Hüseyin, Hüseyin Şirin; Mathematics; MathematicsIn this paper we study the process of Riemann and Lebesgue integration oil time scales. The relationship of the Riemann and Lebesgue integrals is considered and a criterion for Riemann integrability is established. (C) 2003 Elsevier Inc. All rights reserved.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: 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.
