Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives

This paper presents a class ofLp-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 derivatives.

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SHARP INTEGRAL INEQUALITIES BASED ON GENERAL TWO-POINT FORMULAE VIA AN EXTENSION OF MONTGOMERY’S IDENTITY

The ANZIAM Journal ◽

10.1017/s1446181109000315 ◽

2009 ◽

Vol 51 (1) ◽

pp. 67-101 ◽

Cited By ~ 2

Author(s):

A. AGLIĆ ALJINOVIĆ ◽

J. PEČARIĆ ◽

M. RIBIČIĆ PENAVA

Keyword(s):

Integral Inequalities ◽

Quadrature Formulae ◽

Taylor’S Formula ◽

Taylor's Formula

AbstractWe consider families of general two-point quadrature formulae, using the extension of Montgomery’s identity via Taylor’s formula. The formulae obtained are used to present a number of inequalities for functions whose derivatives are fromLpspaces and Bullen-type inequalities.

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Taylor’s formula involving generalized fractional derivatives

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.04.040 ◽

2018 ◽

Vol 335 ◽

pp. 182-195 ◽

Cited By ~ 1

Author(s):

Mondher Benjemaa

Keyword(s):

Fractional Derivatives ◽

Taylor’S Formula ◽

Generalized Fractional Derivatives ◽

Taylor's Formula

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Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2012/343191 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12

Author(s):

J. Pečarić ◽

M. Ribičić Penava

Keyword(s):

Quadrature Formula ◽

Integral Inequalities ◽

Montgomery Identity ◽

Quadrature Formulae ◽

Taylor’S Formula ◽

Special Cases ◽

Taylor's Formula

We consider families of general four-point quadrature formulae using a generalization of the Montgomery identity via Taylor’s formula. The results are applied to obtain some sharp inequalities for functions whose derivatives belong to spaces. Generalizations of Simpson’s 3/8 formula and the Lobatto four-point formula with related inequalities are considered as special cases.

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