Results 1 to 10 of about 750 (182)
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
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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.
Ghulam Farid +4 more
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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 ...
Tao Yan +3 more
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Generalizations of Riemann–Liouville fractional integrals and applications
Mathematical Methods in the Applied SciencesThe 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.
exaly +2 more sources
Further Midpoint Inequalities via Generalized Fractional Operators in Riemann–Liouville Sense
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 +2 more
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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 +5 more
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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>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 +1 more
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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 +2 more
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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 +2 more
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Maclaurin-type inequalities for Riemann-Liouville fractional integrals
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, 2023 The authors give estimates for the modulus of the difference \[ D(f,a,b,\alpha):=\frac{1}{8}\big[3f((5a+b)/6)+2f((a+b)/2)+2f((a+3b)/6)\big]-\frac{\Gamma(\alpha+1)}{2(b-a)^\alpha}\big[J_{a+}^{\alpha} f(b)+J_{b-}^{\alpha} f(a)\big] \] where \(f\in L_1[a,b]\) and \[ J_{a+}^{\alpha}f(x):=\frac{1}{\Gamma(\alpha)}\int_a^x (x-t)^{\alpha-1}f(t)dt,\,\,x>a \] \[
Hezenci, Fatih, BUDAK, HÜSEYİN
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