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Fractional modeling of hepatitis B virus transmission via heterosexual and homosexual contacts and its disability burden. [PDF]

BMC Infect Dis
Guedri K, Zarin R, Makhdoum BM, Niyazi HA, Fadhl BM, Peter OJ.   +5 more
europepmc   +1 more source

Nonlinear wave propagation governed by a fractional derivative. [PDF]

Nat Commun
Hoang VT, Widjaja J, Qiang YL, Liu MK, Alexander TJ, Runge AFJ, de Sterke CM.   +6 more
europepmc   +1 more source

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Approximations of fractional integrals and Caputo fractional derivatives

Applied Mathematics and Computation, 2006
In a series of recent papers [see \textit{K. Diethelm, A. D. Freed} and \textit{N. J. Ford}, Numer. Algorithms 36, No. 1, 31--52 (2004; Zbl 1055.65098)], and the references cited therein], the reviewer and his collaborators have proposed and analysed a numerical scheme for the approximation of \(J^\alpha\), the Riemann-Liouville fractional integral of ...
Zaid Odibat
exaly   +2 more sources

General fractional integrals and derivatives and their applications

Physica D: Nonlinear Phenomena, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuri Luchko
exaly   +2 more sources

Fractional Integrals and Derivatives

Industrial and Applied Mathematics, 2023
K Balachandran, Balachandran K
exaly   +2 more sources

Transients of fractional-order integrator and derivatives

Signal, Image and Video Processing, 2012
Although fractional-order differentiation is generallyconsidered as the basis of fractional calculus, we demonstrate in this paper that the real basis is in fact fractional-order integration, mainly because definition and properties of fractional differentiation rely deeply on fractional integration.
Jean-Claude Trigeassou, Nezha Maamri, Jocelyn Sabatier, Alain Oustaloup   +3 more
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A new fractional integral associated with the Caputo–Fabrizio fractional derivative

Rendiconti del Circolo Matematico di Palermo Series 2, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Moumen Bekkouche, H. Guebbai, M. Kurulay, S. Benmahmoud   +3 more
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Fractional Derivative and Fractional Integral

2018
For every α > 0 and a local integrable function f(t), the right FI of order α is defined: $$\displaystyle{ }_aI_t^\alpha f(t) = \displaystyle\frac {1}{\Gamma (\alpha )}\displaystyle\int _a^t(t - u)^{\alpha - 1}f(u)du,\qquad-\infty \le a < t < \infty .$$
Constantin Milici, Gheorghe Drăgănescu, J. Tenreiro Machado   +2 more
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A Review on Integral Transforms of Fractional Integral and Derivative

International Academic Journal of Science and Engineering, 2022
In this paper, we present a review of the integral transformations of fractional calculus, namely the Riemann-Liouville integral, the Riemann-Liouville derivative, and the Caputo derivative.
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a-times integrated semigroups and fractional derivation

Forum Mathematicum, 2002
The work is devoted to the \(\alpha\)-times integrated semigroups and functional calculus which is related to smooth distribution semigroups. The functional calculus for \(\alpha\)-times integrated semigroups is obtained by applying the fractional integration and derivation to the vector-valued Laplace transform.
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