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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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 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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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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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 generalized Riemann-Liouville k-fractional integral inequalities [PDF]
Journal of Inequalities and Applications, 2016 The focus of the present study is to prove some new Pólya-Szegö type integral inequalities involving the generalized Riemann-Liouville k-fractional integral operator. These inequalities are used then to establish some fractional integral inequalities of Chebyshev type.
Praveen Agarwal +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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On a Fractional Differential Equation with r-Laplacian Operator and Nonlocal Boundary Conditions
Mathematics, 2022 We study the existence and multiplicity of positive solutions of a Riemann-Liouville fractional differential equation with r-Laplacian operator and a singular nonnegative nonlinearity dependent on fractional integrals, subject to nonlocal boundary ...
Johnny Henderson +2 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 M. Carvalho-Neto +1 more
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A Note on Fractional Midpoint Type Inequalities for Co-ordinated (s1, s2)-Convex Functions
Cumhuriyet Science Journal, 2022 In the present paper, some Hermite-Hadamard type inequalities in the case of differentiable co-ordinated (s_1," " s_2)-convex functions are investigated.
Fatih Hezenci
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