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### A new generalization of Ostrowski type inequality on time scales.

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

### Bounds for certain new integral inequalities on time scales.

Advances in Difference Equations [electronic only]

### Existence of a positive solution to a nonlocal semipositone boundary value problem on a time scale

Commentationes Mathematicae Universitatis Carolinae

We consider the existence of at least one positive solution to the dynamic boundary value problem $\begin{array}{cccc}\hfill -{y}^{\Delta \Delta }\left(t\right)& =\lambda f\left(t,y\left(t\right)\right)\text{,}\phantom{\rule{4.0pt}{0ex}}t\in {\left[0,T\right]}_{𝕋}y\left(0\right)\hfill & \hfill ={\int }_{{\tau }_{1}}^{{\tau }_{2}}{F}_{1}\left(s,y\left(s\right)\right)\Delta sy\left({\sigma }^{2}\left(T\right)\right)& ={\int }_{{\tau }_{3}}^{{\tau }_{4}}{F}_{2}\left(s,y\left(s\right)\right)\Delta s,\hfill \end{array}$ where $𝕋$ is an arbitrary time scale with $0<{\tau }_{1}<{\tau }_{2}<{\sigma }^{2}\left(T\right)$ and $0<{\tau }_{3}<{\tau }_{4}<{\sigma }^{2}\left(T\right)$ satisfying ${\tau }_{1}$, ${\tau }_{2}$, ${\tau }_{3}$, ${\tau }_{4}\in 𝕋$, and where the boundary conditions at $t=0$ and $t={\sigma }^{2}\left(T\right)$ can be both nonlinear and nonlocal. This extends some recent results on second-order semipositone dynamic boundary value problems, and we illustrate these extensions with some examples.

### Generalization of an inequality for integral transforms with kernel and related results.

Journal of Inequalities and Applications [electronic only]

### Hybrid approximations via second order combined dynamic derivatives on time scales.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

### Note on an inequality of F. Qi and L. Debnath.

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

### Opial's type inequalities on time scales and some applications

Annales Polonici Mathematici

We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...

### Ostrowski inequalities on time scales.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### Periodicity, almost periodicity for time scales and related functions

Nonautonomous Dynamical Systems

In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.

### Some dynamic inequalities applicable to partial integrodifferential equations on time scales

Archivum Mathematicum

The main objective of the paper is to study explicit bounds of certain dynamic integral inequalities on time scales. Using these inequalities we prove the uniqueness of some partial integrodifferential equations on time scales.

### Theory of rapid variation on time scales with applications to dynamic equations

Archivum Mathematicum

In the first part of this paper we establish the theory of rapid variation on time scales, which corresponds to existing theory from continuous and discrete cases. We introduce two definitions of rapid variation on time scales. We will study their properties and then show the relation between them. In the second part of this paper, we establish necessary and sufficient conditions for all positive solutions of the second order half-linear dynamic equations on time scales to be rapidly varying. Note...

### Time-delay and fractional derivatives.

Advances in Difference Equations [electronic only]

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