Results 31 to 40 of about 1,437,498 (311)

New generalized Pólya–Szegö and Čebyšev type inequalities with general kernel and measure

Advances in Difference Equations, 2020
It is always attractive and motivating to acquire the generalizations of known results. In this article, we introduce a new class C ( h ) $\mathfrak{C(h)}$ of functions which can be represented in a form of integral transforms involving general kernel ...
S. Iqbal, M. Samraiz, Thabet Abdeljawad, Kottakkaran Sooppy Nisar, G. Rahman, M. Adil Khan   +5 more
doaj   +1 more source

Numerical Approaches to Fractional Integrals and Derivatives: A Review

Mathematics, 2020
Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two main characteristics—singularity and nonlocality—has attracted increasing interest due to its potential applications in the real world. This mathematical concept
Minhao Cai, Changpin Li
semanticscholar   +1 more source

Some New Refinements of Hermite–Hadamard-Type Inequalities Involving ψk-Riemann–Liouville Fractional Integrals and Applications

, 2020
The main objective of this article is to establish some new fractional refinements of Hermite–Hadamard-type inequalities essentially using new - Riemann–Liouville fractional integrals, where .
M. U. Awan, Sadia Talib, Y. Chu, M. Noor, K. Noor   +4 more
semanticscholar   +1 more source

Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

Journal of Inequalities and Applications, 2020
In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined
Dafang Zhao, M. Ali, A. Kashuri, H. Budak, M. Sarıkaya   +4 more
semanticscholar   +1 more source

On the weighted fractional Pólya–Szegö and Chebyshev-types integral inequalities concerning another function

Advances in Difference Equations, 2020
The primary objective of this present paper is to establish certain new weighted fractional Pólya–Szegö and Chebyshev type integral inequalities by employing the generalized weighted fractional integral involving another function Ψ in the kernel.
Kottakkaran Sooppy Nisar, Gauhar Rahman, Dumitru Baleanu, Muhammad Samraiz, Sajid Iqbal   +4 more
doaj   +1 more source

On a system of Riemann–Liouville fractional differential equations with coupled nonlocal boundary conditions

Advances in Difference Equations, 2021
We investigate the existence of solutions for a system of Riemann–Liouville fractional differential equations with nonlinearities dependent on fractional integrals, subject to coupled nonlocal boundary conditions which contain various fractional ...
Rodica Luca
doaj   +1 more source

Riemann-Liouville Fractional integral operators with respect to increasing functions and strongly (α,m)-convex functions

AIMS Mathematics, 2021
In this paper Hadamard type inequalities for strongly (α,m)-convex functions via generalized Riemann-Liouville fractional integrals are studied. These inequalities provide generalizations as well as refinements of several well known inequalities.
Ghulam Farid, Hafsa Yasmeen, Hijaz Ahmad, Chahn Yong Jung   +3 more
doaj   +1 more source

The Minkowski inequalities via generalized proportional fractional integral operators

Advances in Difference Equations, 2019
Recent research has gained more attention on conformable integrals and derivatives to derive the various type of inequalities. One of the recent advancements in the field of fractional calculus is the generalized nonlocal proportional fractional ...
Gauhar Rahman, Aftab Khan, Thabet Abdeljawad, Kottakkaran Sooppy Nisar   +3 more
doaj   +1 more source

A comprehensive review of Grüss-type fractional integral inequality

AIMS Mathematics
A survey of results on Grüss-type inequalities associated with a variety of fractional integral and differential operators is presented. The fractional differential operators includes, Riemann-Liouville fractional integral operators, Riemann-Liouville ...
Muhammad Tariq, Sotiris K. Ntouyas, Hijaz Ahmad , Asif Ali Shaikh, Bandar Almohsen , Evren Hincal   +5 more
doaj   +1 more source

Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial

Mathematics, 2019
Several fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions.
R. Garrappa, E. Kaslik, M. Popolizio
semanticscholar   +1 more source