On Opial-type inequalities with higher order partial derivatives

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...

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

On some Opial-type inequalities

* Correspondence: chjzhao@163. com Department of Mathematics, China Jiliang University, Hangzhou 310018, PR China Full list of author information is available at the end of the article Abstract In the present paper we establish some new Opial-type inequalities involving higherorder partial derivatives. Our results in special cases yield some of the recent results on Opial’s inequality and also ...

General Multiple Opial-type Inequalities for the Canavati Fractional Derivatives

In this paper we establish some general multiple Opial-type inequalities involving the Canavati fractional derivatives. In some cases the best possible constants are discussed. 1 Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Split, Croatia. E-mail address: [email protected] 2 Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia. E-mail address:...

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.