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Fractional Integration and Dual Integral Equations
Canadian Journal of Mathematics, 1962In the analysis of mixed boundary value problems by the use of Hankel transforms we often encounter pairs of dual integral equations which can be written in the symmetrical form(1.1)Equations of this type seem to have been formulated first by Weber in his paper (1) in which he derives (by inspection) the solution for the case in which α — β = ½, v = 0,
Erdélyi, Arthur, Sneddon, I. N.
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Fractional Derivative and Fractional Integral
2018For 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 +2 more
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On Fractional Multilinear Singular Integrals
Mathematische Nachrichten, 2002The authors consider the following type of fractional multilinear integrals with rough kernels defined by \[ T_{\Omega,\alpha}^{A}f(x)= \int_{\mathbb R^n}\frac{\Omega(x-y)}{|x-y|^{n-\alpha+m-1}} R_m(A;x,y)f(y) dy, \] where ...
Wu, Qiang, Yang, Dachun
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Interpolational Integral Continued Fractions
Ukrainian Mathematical Journal, 2003For nonlinear functionals determined in the space of piecewise continuous functions an interpolational integral continued fraction by using continual piecewise continuous knots is constructed. Conditions for the existence and uniqueness of interpolants of this kinds are established.
Makarov, V. L. +2 more
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Multilinear Singular and Fractional Integrals
Acta Mathematica Sinica, English Series, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Yong, Lu, Shanzhen, Yabuta, Kôzô
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A Note on the Fractional Integrated Fractional Brownian Motion
Acta Applicandae Mathematica, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximations of fractional integrals and Caputo fractional derivatives
Applied Mathematics and Computation, 2006In 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 ...
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Delay Approximation of Fractional Integrals
Asian Journal of Control, 2012AbstractThis paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag‐Leffler function an approximation of fractional integrals consisting of time delayed samples
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On the Ranges of Certain Fractional Integrals
Canadian Journal of Mathematics, 1972Suppose 1 ≦ P < ∞, μ is real, and denote by Lμ,p the collection of functions f, measurable on (0, ∞ ), and which satisfy1.1Also denote by [X] the collection of bounded operators from a Banach space X to itself. For v > 0, Re α > 0, Re β > 0, let1.2and1.3where ξ and η are complex numbers. Iv,α,ξ and Jv,β,η, are generalizations of the Riemann-
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