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The Relationship between the Box Dimension of Continuous Functions and Their (k,s)-Riemann–Liouville Fractional Integral [PDF]
, 2023 This article is a study on the (k,s)-Riemann–Liouville fractional integral, a generalization of the Riemann–Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furthermore,
Wei Xiao, Bingqian Wang
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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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Methods for Solving Some Fractional Integral [PDF]
, 2023 : In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus, we evaluate some fractional integral. The main methods we used are fractional L’Hospital’s rule, integration by parts for fractional calculus, and a new ...
Chii-Huei Yu
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An Alternative Definition for the k-Riemann-Liouville Fractional Derivative [PDF]
, 2015 Copyright c © 2014 Gustavo Abel Dorrego. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly ...
Dorrego, Gustavo +2 more
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Fractional variational problems with the Riesz-Caputo derivative [PDF]
, 2012 In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the ...
Almeida, R. +2 more
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Assembling classical and dynamic inequalities accumulated on calculus of time scales
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2020 In this paper, we present an extension of dynamic Renyi’s inequality on time scales by using the time scale Riemann–Liouville type fractional integral. Furthermore, we find generalizations of the well–known Lyapunov’s inequality and Radon’s inequality on
Sahir, M.J.S.
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Fractal and Fractional, 2022 First, we show the equivalence of two definitions of the left Riemann–Liouville fractional integral on time scales. Then, we establish and characterize fractional Sobolev space with the help of the notion of left Riemann–Liouville fractional derivative ...
Xing Hu, Yongkun Li
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Examining the Hermite–Hadamard Inequalities for k-Fractional Operators Using the Green Function
Fractal and Fractional, 2023 For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in the literature. In this regard, this paper presents the Hermite–Hadamard inequalities for k-Riemann–Liouville fractional integral operators by
Çetin Yildiz, Luminiţa-Ioana Cotîrlă
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Some results on integral inequalities via Riemann–Liouville fractional integrals [PDF]
Journal of Inequalities and Applications, 2019 In current continuation, we have incorporated the notion of $s- ( {\alpha,m} ) $ -convex functions and have established new integral inequalities. In order to generalize Hermite–Hadamard-type inequalities, some new integral inequalities of Hermite–Hadamard and Simpson type using $s- ( {\alpha,m} ) $ -convex function via Riemann–Liouville fractional ...
LI Xiao-ling +6 more
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Some estimations on continuous random variables for (k, s) −fractional integral operators
Moroccan Journal of Pure and Applied Analysis, 2020 In this work, we establish some new (k, s) −fractional integral inequalities of continuous random variables by using the (k, s) −Riemann-Liouville fractional integral operator.
Houas Mohamed
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