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Fuzzy fractional integral equations under compactness type condition
Fractional Calculus and Applied Analysis, 2012 In this paper we study a fuzzy fractional integral equation. The fractional derivative is considered in the sense of Riemann-Liouville and we establish existence of the solutions of fuzzy fractional integral equations using the Hausdorff measure of ...
Ravi P Agarwal +2 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, 2017zbMATH 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, 2013In 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 +3 more
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Fractional and integral colourings
Mathematical Programming, 1997Let \(G=(V,E)\) 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, 1970Certain 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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Fractional integration: A comparative analysis of fractional integrators
Eighth International Multi-Conference on Systems, Signals & Devices, 2011The 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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Approximations of the Fractional Integral and Numerical Solutions of Fractional Integral Equations
Communications on Applied Mathematics and Computation, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Fractional Integration by Parts
Proceedings of the London Mathematical Society, 1938Let \((a,b)\) 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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