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Some Riemann–Liouville fractional integral inequalities for convex functions
The Journal of Analysis, 2018We are pleased to investigate some Riemann–Liouville fractional integral inequalities in a very simple and novel way. By using convexity of a function f and a simple inequality over the domain of f we establish some interesting results.
G. Farid
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Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions
Fractional Calculus and Applied Analysis, 2018The present paper investigates fractal dimension of fractional integral of continuous functions whose fractal dimension is 1 on [0, 1]. For any continuous functions whose Box dimension is 1 on [0, 1], Riemann-Liouville fractional integral of these ...
Yongshun Liang
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Geometric Interpretation for Riemann–Liouville Fractional-Order Integral
2020 Chinese Control And Decision Conference (CCDC), 2020A new method is proposed to plot the image of Riemann–Liouville (RL) fractional-order integral. The meanings of the image are discussed, including the mathematical expression of the image, the corresponding relationship between the image and RL fractional-order integral, and the change of the image as increasing the upper limit of RL fractional-order ...
Lu Bai, Dingyu Xue, Li Meng
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On the Integral Inequalities for Riemann–Liouville and Conformable Fractional Integrals
2018An 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. +3 more
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The Right Multidimensional Riemann–Liouville Fractional Integral
2016Here we study some important properties of right multidimensional Riemann–Liouville fractional integral operator, such as of continuity and boundedness.
George A. Anastassiou +1 more
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Fractional Order Riemann–Liouville Integral Equations
2012In this chapter, we shall present existence results for some classes of Riemann–Liouville integral equations of two variables by using some fixed-point theorems.
Mouffak Benchohra +2 more
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Diffusive representation of Riemann-Liouville fractional integrals and derivatives
2017 36th Chinese Control Conference (CCC), 2017This paper presents a novel equivalent description of fractional-order integrals and derivatives via an auxiliary integral function of two variables. Employing the concept of Laguerre integration, a novel approximate scheme for the resulting infinite dimensional state space model is derived.
Baoli Ma, Yuxiang Guo
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Dimension of Riemann-Liouville fractional integral of Takagi function
2018 Chinese Control And Decision Conference (CCDC), 2018In this paper, we mainly discuss the characteristics of a type of special function called Takagi function which was derived from Weierstrass function. We have proved this function is continuous but can not be differentiable on any subinterval. In other words, it has no bounded variation points even one.
Yong Shun Liang, Ning Liu, Kui Yao
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Mesoscopic Fractional Kinetic Equations versus a Riemann–Liouville Integral Type [PDF]
, 2007 It is proved that kinetic equations containing noninteger integrals and derivatives are appeared in the result of reduction of a set of micromotions to some averaged collective motion in the mesoscale region. In other words, it means that after a proper statistical average the microscopic dynamics is converted into a collective complex dynamics in the ...
Nigmatullin R., Trujillo J.
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