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Conference Object Citation - WoS: 67Improper Integrals on Time Scales(Dynamic Publishers, inc, 2003) Bohner, M; Guseinov, GSIn this paper we study improper integrals on time scales. We also give some mean value theorems for integrals on time scales, which are used in the proof of an analogue of the classical Dirichlet-Abel test for improper integrals.Article Citation - WoS: 6Citation - Scopus: 6Lyapunov Type Inequalities for Second Order Sub and Super-Half Differential Equations(Dynamic Publishers, inc, 2015) Agarwal, Ravi P.; Ozbekler, Abdullah; MathematicsIn the case of oscillatory potential, we present a Lyapunov type inequality for second order differential equations of the form (r(t)Phi(beta)(x'(t)))' + q(t)Phi(gamma)(x(t)) = 0, in the sub-half-linear (0 < gamma < beta) and the super-half-linear (0 < beta < gamma < 2 beta) cases where Phi(*)(s) = vertical bar s vertical bar*(-1)s.Article Citation - WoS: 26Citation - Scopus: 30Oscillations of First Order Delay Dynamic Equations(Dynamic Publishers, inc, 2006) Sahiner, Y.; Stavroulakis, I. P.Consider the first order linear delay dynamic equation of the forms x(Delta)(t) + p(t)x(tau(t)) = 0. (E) New oscillation criteria are established which contain well-known criteria for delay differential and difference equations as special cases. Illustrative examples are given to show that the results obtained essentially improve known oscillation results for Eq. (E).Article Citation - WoS: 7Citation - Scopus: 8Surface Areas and Surface Integrals on Time Scales(Dynamic Publishers, inc, 2010) Bohner, Martin; Guseinov, Gusein Sh; MathematicsWe 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 integralsArticle Citation - WoS: 88Citation - Scopus: 98Multiple Integration on Time Scales(Dynamic Publishers, inc, 2005) Bohner, M; Guseinov, GS; 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.Article Citation - WoS: 81Citation - Scopus: 92Partial Differentiation on Time Scales(Dynamic Publishers, inc, 2004) Bohner, M; Guseinov, GS; 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.
