Results 11 to 20 of about 2,981 (208)

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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(k,s)-Riemann-Liouville fractional integral and applications [PDF]

Hacettepe Journal of Mathematics and Statistics, 2016
In this paper, we introduce a new approach on fractional integration, which generalizes the Riemann-Liouville fractional integral. We prove some properties for this new approach. We also establish some new integral inequalities using this new fractional integration.
SARIKAYA, Mehmet Zeki, DAHMANI, Zoubir, KIRIS, Mehmet Eyüp, AHMAD, Farooq   +3 more
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On some generalized integral inequalities for Riemann-Liouville fractional integrals [PDF]

Filomat, 2015
In this paper, we give a generalized Montogomery identities for the Riemann-Liouville fractional integrals. We also use this Montogomery identities to establish some new Ostrowski type integral inequalities.
Sarikaya, Mehmet Zeki, Filiz, Hatice, Kiris, Mehmet Eyup   +2 more
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Integral-Type Fractional Equations with a Proportional Riemann–Liouville Derivative [PDF]

Journal of Mathematics, 2021
In this paper, we present the necessary conditions where integral-type fractional equations with a proportional Riemann–Liouville derivative have a unique solution. Also, we give an example to illustrate our work.
Nabil Mlaiki
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New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators [PDF]

Journal of Mathematics, 2020
In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators ...
Qiong Kang, Saad Ihsan Butt, Waqas Nazeer, Mehroz Nadeem, Jamshed Nasir, Hong Yang   +5 more
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Riemann–Liouville Fractional Fundamental Theorem of Calculus and Riemann–Liouville Fractional Polya Integral Inequality and the Generalization to Choquet Integral Case [PDF]

, 2020
Here we present the right and left Riemann–Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time. Then we establish a Riemann–Liouville fractional Polya type integral inequality with the help of generalised right and left Riemann–Liouville fractional derivatives. The amazing fact here is that
Anastassiou, George A., George A. Anastassiou   +1 more
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On the Integral Inequalities for Riemann–Liouville and Conformable Fractional Integrals [PDF]

, 2018
An integral operator is sometimes called an integral transformation. In the fractional analysis, Riemann–Liouville integral operator (transformation) of fractional integral is defined as $$S_{\alpha }(x)= \frac{1}{\Gamma (x)} \int _{0}^{x} (x-t)^{\alpha -1}f(t)dt$$ where f(t) is any integrable function on [0, 1] and \(\alpha >0\), t is in domain
Emin Ozdemir M., Akdemir A.o., Set E., Ekinci A., Akdemir, Ahmet Ocak, Belirlenecek, Emin Ozdemir, M., Education Faculty, Uludag University, Bursa, Turkey; Akdemir, A.O., Faculty of Science and Letters, Agri Ibrahim Cecen University, Agri, Turkey; Set, E., Faculty of Science and Letters, Ordu University, Ordu, Turkey; Ekinci, A., Faculty of Science and Letters, Ordu University, Ordu, Turkey   +6 more
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Estimates of Upper Bound for a Function Associated with Riemann-Liouville Fractional Integral via h-Convex Functions [PDF]

Journal of Function Spaces, 2019
A new identity involving Riemann-Liouville fractional integral is proposed. The result is then used to obtain some estimates of upper bound for a function associated with Riemann-Liouville fractional integral via h-convex functions.
Shan-He Wu, Muhammad Uzair Awan
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On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application [PDF]

Journal of Inequalities and Applications
Post-quantum integral inequalities involving the Riemann–Liouville fractional integral have a significant role in understanding and modeling systems with nonlocal interactions; anomalous diffusion and memory effects make them indispensable for addressing
Sobia Rafeeq, Sabir Hussain, Drakhshan Mansab, Hijaz Ahmad, Taha Radwan   +4 more
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