In this paper, we prove some new generalizations of dynamic Opial-type inequalities on time scales. From these inequalities, as special cases, we formulate some integral and discrete inequalities proved in the literature and also extend some obtained dynamic inequalities on time scales. The main results are proved by using some algebraic inequalities, Holder’s inequality, and a simple consequence of Keller’s chain rule on time scales.

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On some generalizations of dynamic Opial-type inequalities on time scales

Sharp Opial-type inequalities involving $r$-derivatives and their applications

In 2020, El-Deeb et al. proved several dynamic inequalities. It is our aim in this paper to give the retarded time scales case of these inequalities. We also give a new proof and formula of Leibniz integral rule on time scales. Beside that, we also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as special cases. Furthermore, we study boundedness of some delay initial value problems by applying our results as application.

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On some new double dynamic inequalities associated with Leibniz integral rule on time scales

In this paper we shall offer very general Opial-type inequalities involving higher order derivatives of two functions. From these inequalities we then deduce extended and improved versions of several recent results.

Sharp Opial-Type Inequalities Involving Higher Order Derivatives of Two Functions

In this paper we present sharp Opial-type inequalities in two independent variables involving higher order partial derivatives. From the particular cases of our results we then correct as well as improve several recent inequalities.

Li Ju-Da

Papers

Opial-type integral inequalities involving several higher order derivatives