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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.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: 1Citation - Scopus: 2Asymptotic Equivalence of Impulsive Dynamic Equations on Time Scales(Hacettepe Univ, Fac Sci, 2023) Akgol, Sibel DogruThe asymptotic equivalence of linear and quasilinear impulsive dynamic equations on time scales, as well as two types of linear equations, are proven under mild conditions. To establish the asymptotic equivalence of two impulsive dynamic equations a method has been developed that does not require restrictive conditions, such as the boundedness of the solutions. Not only the time scale extensions of former results have been obtained, but also improved for impulsive differential equations defined on the real line. Some illustrative examples are also provided, including an application to a generalized Duffing equation.Article Citation - WoS: 9Citation - Scopus: 10A Solution To Nonlinear Volterra Integro-Dynamic Equations Via Fixed Point Theory(Univ Nis, Fac Sci Math, 2019) Sevinik-Adiguzel, Rezan; Karapinar, Erdal; Erhan, Inci M.In this paper we discuss the existence and uniqueness of solutions of a certain type of nonlinear Volterra integro-dynamic equations on time scales. We investigate the problem in the setting of a complete b-metric space and apply a fixed point theorem with a contractive condition involving b-comparison function. We use the theorem to show the existence of a unique solution of some particular integro-dynamic equations.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.
