منابع مشابه
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.
متن کاملOn 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 ...
متن کاملSome Opial-Type Inequalities on Time Scales
and Applied Analysis 3 where r t is positive and continuous function with ∫X a dt/r t < ∞, and if x b 0, then ∫b X |x t |∣∣x′ t ∣∣dt ≤ 1 2 ∫b
متن کاملOPIAL 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...
متن کاملOpial inequalities on time scales
We present a version of Opial’s inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1986
ISSN: 0022-247X
DOI: 10.1016/0022-247x(86)90176-9