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Bounds of Riemann-Liouville Fractional Integrals in General Form via Convex Functions and Their Applications

Mathematics, 2018
In this article, we establish bounds of sum of the left and right sided Riemann Liouville (RL) fractional integrals and related inequalities in general form.
Muhammad Shoaib Saleem, Ghulam Farid, Shin Min Kang   +2 more
exaly   +4 more sources

On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity

Fractal and Fractional, 2022
In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann ...
Ghulam Farid, Chahn Yong Jung, Yan Tao
exaly   +4 more sources

On the Hermite–Hadamard type inequality for ψ-Riemann–Liouville fractional integrals via convex functions

Journal of Inequalities and Applications, 2019
In this paper, we establish a new Hermite–Hadamard inequality involving left-sided and right-sided ψ-Riemann–Liouville fractional integrals via convex functions.
Donal O'Regan, JinRong Wang
exaly   +4 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

On New Inequalities via Riemann-Liouville Fractional Integration [PDF]

Abstract and Applied Analysis, 2012
We extend the Montgomery identities for the Riemann-Liouville fractional integrals. We also use these Montgomery identities to establish some new integral inequalities.
Mehmet Zeki Sarikaya, Hasan Ogunmez
doaj   +6 more sources

Generalizations of Riemann–Liouville fractional integrals and applications

Mathematical Methods in the Applied Sciences
The notion of a generalized Riemann–Liouville fractional integral is introduced, and its domain, range, and properties are studied. The new notion and properties provide new insight and understanding into the classical Riemann–Liouville fractional integral and its properties.
Kunquan Lan
exaly   +2 more sources

Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions

Journal of Function Spaces, 2022
In this paper, we establish some new Newton’s type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several
Jarunee Soontharanon, Muhammad Aamir Ali, Hüseyin Budak, Pinar Kösem, Kamsing Nonlaopon, Thanin Sitthiwirattham   +5 more
doaj   +1 more source

The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces I

Communications on Pure and Applied Analysis, 2022
<p style='text-indent:20px;'>In this paper we study the Riemann-Liouville fractional integral of order <inline-formula><tex-math id="M1">\begin{document}$ \alpha&gt;0 $\end{document}</tex-math></inline-formula> as a linear operator from <inline-formula><tex-math id="M2">\begin{document}$ L^p(I,X) $\end ...
Paulo Mendes Carvalho Neto, Renato Fehlberg Júnior   +1 more
openaire   +6 more sources

A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators

Axioms, 2023
A review of the results on the fractional Fejér-type inequalities, associated with different families of convexities and different kinds of fractional integrals, is presented.
Muhammad Tariq, Sotiris K. Ntouyas, Asif Ali Shaikh   +2 more
doaj   +1 more source

Some New Riemann-Liouville Fractional Integral Inequalities [PDF]

International Journal of Mathematics and Mathematical Sciences, 2014
In this paper, some new fractional integral inequalities are established.
Jessada Tariboon, Sotiris K. Ntouyas, Weerawat Sudsutad   +2 more
openaire   +3 more sources