Results 151 to 160 of about 1,528 (178)

Rational Approximations of Riemann--Liouville and Weyl Fractional Integrals

Mathematical Notes, 2005
Given \(h\) an \(L_1\)-integrable function on \(I= [a, b]\) and \(\alpha> 0\), set \(f(x)= (P^\alpha_\pm* h)(x)\) where \(P^\alpha_\pm(t)\) denotes either the well known Riemann-Liouville kernel or the Weyl kernel when \(I= [0, 2\pi]\) and \(h\) is a \(2\pi\)-periodic function. Here \(*\) represents the usual ``convolution'' operation.
openaire   +1 more source

On the Integral Inequalities for Riemann–Liouville and Conformable Fractional Integrals

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.   +3 more
openaire   +4 more sources

Generalized Fractional Ostrowski's Type Inequalities Involving Riemann-Liouville Fractional Integration

2020
Fractional calculus has applications in many practical problems such as electromagnetic waves, visco-elastic systems, quantum evolution of complex systems, diffusion waves, physics, engineering, finance, social sciences, economics, mathematical biology, and chaos theory.
Ather Qayyum, Muhammad Shoaib
openaire   +1 more source

Random inequalities via Riemann-Liouville fractional integration

Journal of Interdisciplinary Mathematics, 2021
Mohamed Bezziou, Zoubir Dahmani
openaire   +1 more source

Mesoscopic Fractional Kinetic Equations versus a Riemann–Liouville Integral Type

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.
openaire   +3 more sources

The Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative on Time Scales

2018
In this chapter we suppose that \(\mathbb {T}\) is a time scale with forward jump operator and delta differentiation operator σ and Δ, respectively.
openaire   +1 more source

Hermite–Hadamard type inequalities for multiplicative Riemann–Liouville fractional integrals

Journal of Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tingsong Du, Yu Peng
openaire   +1 more source

The Solutions of Some Riemann–Liouville Fractional Integral Equations

Fractal and Fractional, 2021
Karuna Kaewnimit, Fongchan Wannalookkhee, Kamsing Nonlaopon   +2 more
exaly  

Analysis of fractal dimension of mixed Riemann-Liouville integral

Numerical Algorithms, 2022
Subhash Chandra, Syed Abbas
exaly  

On Solutions of Fractional Integrodifferential Systems Involving Ψ-Caputo Derivative and Ψ-Riemann–Liouville Fractional Integral

Mathematics, 2023
Abdelkader Moumen, Jehad Alzabut, Mhamed Benaissa   +2 more
exaly