Results 11 to 20 of about 1,935,396 (342)

Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals [PDF]

Journal of Inequalities and Applications, 2017
Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named ( k , s ) $(k,s)$ -Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established.
Praveen Agarwal, Mohamed Jleli, Muharrem Tomar   +2 more
doaj   +6 more sources

General Fractional Integrals and Derivatives with the Sonine Kernels [PDF]

Mathematics, 2021
In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero.
Yuri Luchko
doaj   +4 more sources

The General Fractional Integrals and Derivatives on a Finite Interval

Mathematics, 2023
The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis.
Mohammed Al-Refai, Yuri Luchko
doaj   +4 more sources

On multiplicative conformable fractional integrals: theory and applications [PDF]

Boundary Value Problems
In this paper, we first introduce the multiplicative conformable left and right fractional integrals, followed by the derivation of key properties, such as integrability, boundedness, continuity, and the semi-group property, for the newly defined ...
Hüseyin Budak, Büşra Betül Ergün
doaj   +3 more sources

General Fractional Integrals and Derivatives of Arbitrary Order [PDF]

Symmetry, 2021
In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases.
Yuri Luchko
exaly   +2 more sources

Properties for ψ-Fractional Integrals Involving a General Function ψ and Applications

Mathematics, 2019
In this paper, we are concerned with the ψ-fractional integrals, which is a generalization of the well-known Riemann−Liouville fractional integrals and the Hadamard fractional integrals, and are useful in the study of various fractional ...
Jin Liang, Yunyi Mu
doaj   +2 more sources

Further Midpoint Inequalities via Generalized Fractional Operators in Riemann–Liouville Sense [PDF]

Fractal and Fractional, 2022
In this study, new midpoint-type inequalities are given through recently generalized Riemann–Liouville fractional integrals. Foremost, we present an identity for a class of differentiable functions including the proposed fractional integrals.
Abd-Allah Hyder, Hüseyin Budak, Areej A. Almoneef   +2 more
doaj   +2 more sources

Ostrowski type inequalities involving conformable fractional integrals [PDF]

J Inequal Appl, 2018
In the article, we establish several Ostrowski type inequalities involving the conformable fractional integrals. As applications, we find new inequalities for the arithmetic and generalized logarithmic means.
M. Adil Khan, Sumbel Begum, Yousaf Khurshid, Yu-Ming Chu   +3 more
semanticscholar   +2 more sources

Generalized Riemann-Liouville k -Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities

IEEE Access, 2018
Ostrowski inequality provides the estimation of a function to its integral mean. It is useful in error estimations of quadrature rules in numerical analysis.
Ghulam Farid, Young Chel Kwun, Shin Min Kang   +2 more
exaly   +2 more sources

Newton-type Inequalities for Fractional Integrals by Various Function Classes [PDF]

Universal Journal of Mathematics and Applications
The authors of the paper examine some Newton-type inequalities for various function classes using Riemann-Liouville fractional integrals. Namely, we establish some Newton-type inequalities for bounded functions by fractional integrals.
Hüseyin Budak, Tingsong Du, Fatih Hezenci   +2 more
doaj   +2 more sources