Dynamic Inequalities of Two-Dimensional Hardy Type via Alpha-Conformable Derivatives on Time Scales

Time Scales Hardy–type Inequalities via Superquadracity

In this paper some new Hardy–type inequalities on time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardy–type inequalities involving superquadratic functions with general kernels to the case with arbitrary time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and disc...

Hardy–Leindler Type Inequalities on Time Scales

In this paper, we will prove some new dynamic inequalities on a time scale T. These inequalities, as special cases, when T= R contain some integral inequalities and when T= N contain the discrete inequalities due to Leindler. The main results will be proved by using the Hölder inequality and a simple consequence of Keller’s chain rule on time scales. From our results, as applications, we will d...

Hardy Type Inequalities on Time Scales

Nonlinear Dynamic Inequalities of Gronwall-Bellman Type on Time Scales

The main aim of this paper is to establish some new explicit bounds of solutions of a certain class of nonlinear dynamic inequalities (with and without delays) of Gronwall-Bellman type on a time scale T which is unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of delay dynami...

Diamond-alpha Integral Inequalities on Time Scales

The theory of the calculus of variations was recently extended to the more general time scales setting, both for delta and nabla integrals. The primary purpose of this paper is to further extend the theory on time scales, by establishing some basic diamond-alpha dynamic integral inequalities. We prove generalized versions of Hölder, Cauchy-Schwarz, Minkowski, and Jensen’s inequalities. For the ...