3,769 research outputs found
The Natural Logarithm on Time Scales
We define an appropriate logarithm function on time scales and present its
main properties. This gives answer to a question posed by M. Bohner in [J.
Difference Equ. Appl. {\bf 11} (2005), no. 15, 1305--1306].Comment: 6 page
Higher-Order Calculus of Variations on Time Scales
We prove a version of the Euler-Lagrange equations for certain problems of
the calculus of variations on time scales with higher-order delta derivatives.Comment: Corrected minor typo
A generalization of Ostrowski inequality on time scales for k points
In this paper we first generalize the Ostrowski inequality on time scales for
k points and then unify corresponding continuous and discrete versions. We also
point out some particular Ostrowski type inequalities on time scales as special
cases.Comment: 10 page
Complex-valued fractional derivatives on time scales
We introduce a notion of fractional (noninteger order) derivative on an
arbitrary nonempty closed subset of the real numbers (on a time scale). Main
properties of the new operator are proved and several illustrative examples
given.Comment: This is a preprint of a paper whose final and definite form will
appear in Springer Proceedings in Mathematics & Statistics, ISSN: 2194-1009.
Accepted for publication 06/Nov/201
A General Backwards Calculus of Variations via Duality
We prove Euler-Lagrange and natural boundary necessary optimality conditions
for problems of the calculus of variations which are given by a composition of
nabla integrals on an arbitrary time scale. As an application, we get
optimality conditions for the product and the quotient of nabla variational
functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010;
accepted for publication 08-July-201
Halanay type inequalities on time scales with applications
This paper aims to introduce Halanay type inequalities on time scales. By
means of these inequalities we derive new global stability conditions for
nonlinear dynamic equations on time scales. Giving several examples we show
that beside generalization and extension to q-difference case, our results also
provide improvements for the existing theory regarding differential and
difference inequalites, which are the most important particular cases of
dynamic inequalities on time scales
Noether's Theorem on Time Scales
We show that for any variational symmetry of the problem of the calculus of
variations on time scales there exists a conserved quantity along the
respective Euler-Lagrange extremals.Comment: Partially presented at the 6th International ISAAC Congress, August
13 to August 18, 2007, Middle East Technical University, Ankara, Turke
Optimality conditions for the calculus of variations with higher-order delta derivatives
We prove the Euler-Lagrange delta-differential equations for problems of the
calculus of variations on arbitrary time scales with delta-integral functionals
depending on higher-order delta derivatives.Comment: Submitted 26/Jul/2009; Revised 04/Aug/2010; Accepted 09/Aug/2010; for
publication in "Applied Mathematics Letters
Symmetric Differentiation on Time Scales
We define a symmetric derivative on an arbitrary nonempty closed subset of
the real numbers and derive some of its properties. It is shown that
real-valued functions defined on time scales that are neither delta nor nabla
differentiable can be symmetric differentiable.Comment: This is a preprint of a paper whose final and definite form will be
published in Applied Mathematics Letters. Submitted 30-Jul-2012; revised
07-Sept-2012; accepted 10-Sept-201
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