Browsing by Author "Bohner,M."
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Article Citation Count: 6The Euler method for dynamic equations on time scales(Cambridge Scientific Publishers, 2021) Bohner,M.; Erhan,İ.M.; Georgiev,S.G.In this paper, we generalize the Euler method for dynamic equations on time scales. We give estimates for the local and global truncation errors. We apply the method to specimen examples and provide numerical results to support our theoretical discussion. © 2021. All Rights Reserved.Book Citation Count: 19Lyapunov Inequalities and Applications(Springer International Publishing, 2021) Özbekler, Abdullah; Bohner,M.; Özbekler,A.; MathematicsThis book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov's inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content. © Springer Nature Switzerland AG 2021. All rights reserved.Article Citation Count: 90Multiple integration on time scales(2005) Hüseyin, Hüseyin Şirin; Guseinov,G.Sh.; MathematicsIn this paper an introduction to integration theory for multivariable functions on time scales is given. Such an integral calculus can be used to develop a theory of partial dynamic equations on time scales in order to unify and extend the usual partial differential equations and partial difference equations. © Dynamic Publishers, Inc.Article Citation Count: 91Partial differentiation on time scales(2004) Hüseyin, Hüseyin Şirin; Guseinov,G.Sh.; MathematicsIn this paper a differential calculus for multivariable functions on time scales is presented. Such a calculus can be used to develop a theory of partial dynamic equations on time scales in order to unify and extend the usual partial differential and partial difference equations.Article Citation Count: 7Surface areas and surface integrals on time scales(2010) Bohner,M.; Guseinov,G.S.H.We study surfaces parametrized by time scale parameters, obtain an integral fomula for computing the area of time scale surfaces, introduce delta integrals over time scale surfaces, and give sufficient conditions that ensure existence of these integrals. © Dynamic Publishers, Inc.