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Synergistic Integration of Multimodal Lasers and Bioactive Substances for Severe Post-traumatic Facial Sequelae and Traumatic Tattooing: A Case Report. [PDF]

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Szlachcic A, Szlachcic B, Martinelli D, Zevini A, Barini R.   +4 more
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Fractional Integrals of Fractional Fourier Transform for Integrable Boehmians

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Singh, Abhishek, Banerji, P. K.
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What is Fractional Integration? [PDF]

Review of Economics and Statistics, 1999
A simple construction that will be referred to as an error-duration model is shown to generate fractional integration and long memory. An error-duration representation also exists for many familiar ARMA models, making error duration an alternative to autoregression for explaining dynamic persistence in economic variables.
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On the integration of differential fractions

Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, 2013
In this paper, we provide a differential algebra algorithm for integrating fractions of differential polynomials. It is not restricted to differential fractions that are the derivatives of other differential fractions. The algorithm leads to new techniques for representing differential fractions, which may help converting differential equations to ...
François Boulier, François Lemaire, Georg Regensburger, Markus Rosenkranz   +3 more
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Fractional integration: A comparative analysis of fractional integrators

Eighth International Multi-Conference on Systems, Signals & Devices, 2011
The fractional integrator is certainly the key operator of fractional calculus, because of its fundamental applications in Fractional Differential Equation simulation and for the definition of fractional initial conditions. Fractional integration is defined by the classical Riemman-Liouville integral, derived from repeated integration. Three approaches
J.-C Trigeassou, A Oustaloup
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Fractional and integral colourings

Mathematical Programming, 1997
Let \(G=(V,E)\) be an undirected graph and \(c\) any vector in \(\mathbb{Z}^{V(G)}_+\). Denote by \(\chi(G_c)\) and \(\eta(G_c)\) the chromatic number and fractional chromatic number respectively, of \(G\) with respect to \(c\). In this paper graphs are studied for which \(\chi(G_c)-\lceil\eta(G_c)\rceil\leq 1\).
Kilakos, K., Marcotte, O.
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Fractional Integrals of Distributions

SIAM Journal on Mathematical Analysis, 1970
Certain operators of fractional integration arising in connection with singular differential operators, Hankel transforms, and dual integral equations involve integration of fractional order with respect to $r^2$ and multiplication of functions by fractional powers of the independent variable. Such operations are not meaningful for distributions.
Erdélyi, Arthur, McBride, A. C.
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Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations

Communications on Applied Mathematics and Computation, 2021
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On Fractional Integration by Parts

Proceedings of the London Mathematical Society, 1938
Let \((a,b)\) be a finite interval, \(f\in L(a,b)\), \(\alpha>0\), \[ f_\alpha^+\equiv f_\alpha^+(a,x) = (\Gamma(\alpha))^{-1} \int_a^x f(t)(x-t)^{\alpha-1}\,dt, \; f_\alpha^-\equiv f_\alpha^-(a,x) = (\Gamma(\alpha))^{-1} \int_x^b f(t)(t-x)^{\alpha-1}\,dt. \] As a consequence of results of Hardy and Littlewood the authors prove that if \(p>1\), \(q>1\),
Love, E. R., Young, L. C.
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