Opial-type integral inequalities involving several higher order derivatives

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

On Opial–type Integral Inequalities and Applications

In the present paper we establish some new Opial-type inequalities involving higher order partial derivatives. Our results in special cases yield some of the recent results on Opial’s inequality. As application, we prove the uniqueness of the solution of initial value problem involving higher order partial differential equation. Mathematics subject classification (2010): 26D15.

OPIAL TYPE Lp-INEQUALITIES FOR FRACTIONAL DERIVATIVES

This paper presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor’s formula, which enables us to relax restrictions on the orders of fractional deriv...

Sharp Integral Inequalities Involving High-Order Partial Derivatives

Inequalities involving functions of n independent variables, their partial derivatives, integrals play a fundamental role in establishing the existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations 1–10 . Especially, in view of wider applications, inequalities due to Agarwal, Opial, Pachpatte, Wirtinger, Poi...

Opial–type Inequalities for Fractional Integral Operator Involving Mittag––leffler Function

In this paper we give generalization of Opial-type inequalities by using generalized fractional integral operator involving generalized Mittag–Leffler function. We deduce some results which already have been proved. Also we consider n -exponential convexity of some non-negative differences of inequalities involving Mittag-Leffler function and deduce their exponential convexity and log-convexity.