Some New Opial Dynamic Inequalities with Weighted Functions on Time Scales

Dynamic Systems and Applications 24 (2015) 229-242 IMPROVEMENTS OF DYNAMIC OPIAL-TYPE INEQUALITIES AND APPLICATIONS

ABSTRACT. In this paper, we present some new improvements of dynamic Opial-type inequalities of first and higher order on time scales. We employ the new inequalities to prove several results related to the spacing between consecutive zeros of a solution and/or a zero of its derivative of a second-order dynamic equation with a damping term. The main results are proved by making use of a recently...

Some new variants of interval-valued Gronwall type inequalities on time scales

By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.

Dynamic Opial diamond-α integral inequalities involving the power of a function

In this paper, we present some new dynamic Opial-type diamond alpha inequalities on time scales. The obtained results are related to the function [Formula: see text].

Generalized diamond-a dynamic opial inequalities

* Correspondence: billur@cankaya. edu.tr Department of Mathematics and Computer Science, Çankaya University, Ankara, Turkey Full list of author information is available at the end of the article Abstract We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial’s inequality and also provide new esti...

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales