An introduction to difference equations
An introduction to difference equations
Quadratic functionals for second order matrix equations on time scales
Non-Linear Analysis
Positivity of Block Tridiagonal Matrices
SIAM Journal on Matrix Analysis and Applications
Sturm-Liouville eigenvalue problems on time scales
Applied Mathematics and Computation
Journal of Computational and Applied Mathematics - Fixed point theory with applications in nonlinear analysis
Nonlinear boundary value problems on time scales
Nonlinear Analysis: Theory, Methods & Applications
Time scale boundary value problems on infinite intervals
Journal of Computational and Applied Mathematics - Dynamic equations on time scales
Oscillation criteria for second-order matrix dynamic equations on a time scale
Journal of Computational and Applied Mathematics - Dynamic equations on time scales
A third-order differential equation on a time scale
Mathematical and Computer Modelling: An International Journal
Positive solutions for a nonlinear differential equation on a measure chain
Mathematical and Computer Modelling: An International Journal
Asymptotic properties of solutions of a 2nth-order differential equation on a time scale
Mathematical and Computer Modelling: An International Journal
Linear Hamiltonian systems on time scales: Positivity of quadratic functionals
Mathematical and Computer Modelling: An International Journal
Stability for time varying linear dynamic systems on time scales
Journal of Computational and Applied Mathematics
Oscillation criteria of second-order half-linear dynamic equations on time scales
Journal of Computational and Applied Mathematics
Oscillation of second-order nonlinear neutral delay dynamic equations on time scales
Journal of Computational and Applied Mathematics
Positive Solutions of Two-point right focal boundary value problems on time scales
Computers & Mathematics with Applications
Triple positive solutions for some second-order boundary value problem on a measure chain
Computers & Mathematics with Applications
Stability criteria for impulsive systems on time scales
Journal of Computational and Applied Mathematics
Oscillation criteria for two-dimensional dynamic systems on time scales
Journal of Computational and Applied Mathematics
Solvability of Sturm-Liouville problems on time scales at resonance
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
A note on the matrix solutionof the problem XΔ = AX, X(t0) = I
Computers & Mathematics with Applications
Neural Processing Letters
Stability for time varying linear dynamic systems on time scales
Journal of Computational and Applied Mathematics
Oscillation criteria of second-order half-linear dynamic equations on time scales
Journal of Computational and Applied Mathematics
Oscillation of second-order nonlinear neutral delay dynamic equations on time scales
Journal of Computational and Applied Mathematics
Generalization of Ostrowski and Ostrowski-Grüss type inequalities on time scales
Computers & Mathematics with Applications
Oscillation of second-order half-linear delay dynamic equations with damping on time scales
Journal of Computational and Applied Mathematics
Qualitative behavior of SIS epidemic model on time scales
ASM'10 Proceedings of the 4th international conference on Applied mathematics, simulation, modelling
Oscillation of second-order nonlinear delay dynamic equations on time scales
Computers & Mathematics with Applications
The effect of time scales on SIS epidemic model
WSEAS Transactions on Mathematics
Stability of neural networks with both impulses and time-varying delays on time scale
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Function series theory of time scales
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Mathematica applications on time scales
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Mathematical and Computer Modelling: An International Journal
Positive solutions of the singular semipositone boundary value problem on time scales
Mathematical and Computer Modelling: An International Journal
On controllability and observability for a class of linear impulsive dynamic systems on time scales
Mathematical and Computer Modelling: An International Journal
Oscillatory behavior of third-order nonlinear delay dynamic equations on time scales
Journal of Computational and Applied Mathematics
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The study of dynamic equations on time scales, which goes back to its founder Stefan Hilger (1988), is an area of mathematics that has recently received a lot of attention. It has been created in order to unify the study of differential and difference equations. In this paper we give an introduction to the time scales calculus. We also present various properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equations of first order. Several examples and applications, among them an insect population model, are considered. We then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients. Finally, we consider self-adjoint equations and, more generally, so-called symplectic systems, and present several results on the positivity of quadratic functionals.