Compactness of Riemann–Liouville fractional integral operators [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2020 We obtain results on compactness of two linear Hammerstein integral operators with singularities, and apply the results to give new proof that Riemann–Liouville fractional integral operators of order $\alpha\in (0,1)$ map $L^{p}(0,1)$ to $C[0,1]$ and ...
Kunquan Lan
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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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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 ...
Renato Fehlberg Junior
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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.
Praveen Agarwal +2 more
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On the set of solutions of fractional order Riemann–Liouville integral inclusions
Demonstratio Mathematica, 2013 Abstract In this paper, we prove the arcwise connectedness of the solution set of a nonclosed, nonconvex Fredholm type, Riemann–Liouville integral inclusion of fractional order.
Abbas Said, Mouffak Benchohra
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Well-posedness of the initial-boundary value problems for the time-fractional degenerate diffusion equations [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 This paper deals with the solving of initial-boundary value problems for the one-dimensional linear timefractional diffusion equations with time-degenerate diffusive coefficients tβ with β>1-α.
A.G. Smadiyeva
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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, Hüseyin
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Numerical Approximations of the Riemann–Liouville and Riesz Fractional Integrals
Informatica, 2023 In this paper, the numerical algorithms for calculating the values of the left- and right-sided Riemann–Liouville fractional integrals and the Riesz fractional integral using spline interpolation techniques are derived. The linear, quadratic and three variants of cubic splines are taken into account.
Mariusz Ciesielski, Grzegorz Grodzki
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