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Hermite–Hadamard inequalities for Riemann–Liouville fractional integrals [PDF]

Mathematica Slovaca
Abstract In this paper, we prove some new inequalities of Hermite–Hadamard type for differentiable functions with h-convex derivatives. It is also shown that the newly established inequalities are extension of the existing inequalities in the literature. Finally, we give applications of the new results and outline some future problems.
Ali Muhammad Aamir, Kórus Péter, Nápoles Valdés Juan E.   +2 more
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Some Generalized Hadamard–Type Inequalities via Fractional Integrals

Russian Mathematics, 2021
In this paper, the authors derived and proved some generalized inequalities of Hermite-Hadamard type using fractional Riemann-Liouville integrals for the class of s-convex functions.
BAYRAKTAR, BAHTİYAR, Kudaev, Valery, Attaev, Anatoly   +2 more
openaire   +2 more sources

The Hadamard Inequality For Convex Function Via Fractional Integrals

Acta Mathematica Scientia, 2013
Abstract In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
ÖZDEMİR, MUHAMET EMİN, DRAGOMIR, SEVER SILVESTRU, YILDIZ, Çetin   +2 more
openaire   +3 more sources

Fractional integral problems for Hadamard–Caputo fractional Langevin differential inclusions

Journal of Applied Mathematics and Computing, 2015
The authors consider the differential inclusion (of fractional type) \[ D^{\alpha}\big(D^{\beta}+\lambda\big)x(t)\in F\big(t,x(t)\big) \] for \(t\in[1,e]\). The differential inclusion is subjected to the conditions (of nonlocal type) \[ \sum_{i=1}^{m}\theta_{i}I^{\mu_i}x\left(\eta_i\right)=\sum_{j=1}^{n}\phi_{j}I^{\gamma_j}x\left(\omega_j\right) \] and
Ntouyas, Sotiris K., Tariboon, Jessada
openaire   +1 more source

On pseudo-fractional integral inequalities related to Hermite–Hadamard type

Soft Computing, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maryam Hosseini, Azizollah Babakhani, Hamzeh Agahi, Sayyed Hashem Rasouli   +3 more
openaire   +2 more sources

Variational problems with Hadamard type fractional integrals

ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014, 2014
This paper is devoted to the study of variational problems with Hadamard type fractional integrals. We present two approaches to solve such type of variational problems: indirect and direct. In the first case we derive necessary optimality conditions which reduce the problem to one involving a fractional integral equation.
Ricardo Almeida, Agnieszka B. Malinowska, M. Luisa Morgado   +2 more
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On Hadamard Fractional Integral and Physical Interpretation

SSRN Electronic Journal, 2022
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Some New Results on Hermite–Hadamard–Mercer-Type Inequalities Using a General Family of Fractional Integral Operators

Fractal and Fractional, 2021
Erhan Set, Barış çelik
exaly  

Investigation of a Coupled System of Hilfer–Hadamard Fractional Differential Equations with Nonlocal Coupled Hadamard Fractional Integral Boundary Conditions

Fractal and Fractional, 2023
Bashir Ahmad, Shorog Al-Joudi
exaly  

Some New Versions of Hermite–Hadamard Integral Inequalities in Fuzzy Fractional Calculus for Generalized Pre-Invex Functions via Fuzzy-Interval-Valued Settings

Fractal and Fractional, 2022
Muhammad Bilal Khan, Muhammed Aslam Noor, Nehad Ali Shah   +2 more
exaly