On Time Scales
Bounds of Certain Dynamic Inequalities on Time Scales
... of time scale in his Ph.D dissertation. Dynamic inequalities on time scales has applications in various ...on time scales, its properties and applications [1, 5, 6, 7, 8, 9, 10, 11, 12, ...
6
Study of nonlinear Pachpatte’s inequalities on time scales
... Modeling of some real world problem requires using a dynamic system which involves both discrete and continuous times. This is natural to see whether it is feasible to give a framework which permits us to incorporate ...
18
Surfaces on time scales and their metric properties
... Detailed proofs of chain rule theorems and significant remarks can be found in []. In [], vector fields and covariant delta derivatives on time scales are studied for higher di- mensional time ...
10
Steffensen's Integral Inequality on Time Scales
... The aim of this paper is to extend some generalizations of Steffensen’s integral in- equality to an arbitrary time scale. We obtain Steffensen’s integral inequality using the diamond-α derivative on time ...
10
Exponential stability of dynamic equations on time scales
... we use Lyapunov-type functions on time scales and then formulate appropriate inequal- ities on these functions that guarantee that the trivial solution to (1.1) is exponentially or uniformly exponentially ...
12
Diamond Jensen's Inequality on Time Scales
... on time scales have recently received considerable ...time scales. We prove a generalized version of Jensen’s inequality on time scales via the diamond-α integral and present ...
13
Hermite Hadamard Inequality on Time Scales
... Recently, new developments of the theory and applications of dynamic derivatives on time scales were made. The study provides an unification and an extension of traditional differential and difference ...
24
Generalized integral inequalities on time scales
... on time scales which was formulated by Hilger is an area of mathematics which is currently receiving profuse ...times scales is to bring together the study of difference and differential equations, it ...
12
Uniform Lacunary Statistical Convergence on Time Scales
... The measure theory on time scales was first constructed by Guseinov [19] and Lebesque ∆-integral on time scales introduced by Cabada and Vivero [6]. Now, we introduce m-uniform strongly p- ...
8
Periodic boundary value problems on time scales
... We will use the Schauder fixed point theorem and the concept of lower and upper so- lutions to prove the existence of solutions of (1.10). First we prove the existence of the solution for the modified problem with ...
12
Unification of probability theory on time scales
... on time scales, we can define an exponential probability density function in a general case and we can define a moment generating function by us- ing Laplace transformations on time ...on time ...
13
Impulsive Diffusion Equation on Time Scales
... As can be seen from the literature, the studies about spectral theory on time scales have focused on SL equation and Dirac system. We notice that there isn’t any research about impulsive diffusion equation ...
12
Aumann Integral on Time Scales
... In this paper, we consider by the first time the Aumann integral on time scales. Hence, we introduce the Aumann ∆-integral on time scales. We also have established properties for the ...
6
Sobolev’s embedding on time scales
... Sobolev spaces are among the fundamental tools of functional analysis. They are used in variational methods to solve ordinary/partial differential equations or difference equa- tions. In spite of this, the theory for ...
11
Asymptotic stability for dynamic equations on time scales
... Exponential decay and stability of solutions of dynamic equations on time scales were investigated in recent papers [1, 5–7, 11, 12] using Lyapunov’s method. We use different approaches based on integral ...
17
On The Convergence of Stability Domain on Time Scales
... The paper is organized as follows. Section 2 summarizes some preliminary results on time scales, property of exponential functions on time scales and characterizes the stability domain of a ...
12
Boundedness in functional dynamic equations on time scales
... Using nonnegative definite Lyapunov functionals, we prove general theorems for the boundedness of all solutions of a functional dynamic equation on time scales. We ap- ply our obtained results to linear and ...
18
Multiple Lebesgue integration on time scales
... on time scales allows to develop a theory of dynamic equations in order to unify and extend the usual differential equations and difference ...on time scales, we refer the reader to the ...
12
Stability of Linear Dynamic Systems on Time Scales
... Remark 3.16. P ¨otzsche et al. 12 proved a necessary and sufficient condition for the exponential stability of time-variant linear systems on time scales in terms of the eigenvalues of the system ...
12
Basic properties of Sobolev's spaces on time scales
... arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolev’s spaces of functions defined on an arbitrary open interval of the real numbers are ...
14