Results 131 to 140 of about 40,863 (167)

Fractional Integration and Dual Integral Equations

Canadian Journal of Mathematics, 1962
In 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

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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On Fractional Multilinear Singular Integrals

Mathematische Nachrichten, 2002
The 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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A Note on the Fractional Integrated Fractional Brownian Motion

Acta Applicandae Mathematica, 2003
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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 ...
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Interpolational Integral Continued Fractions

Ukrainian Mathematical Journal, 2003
For 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., Khlobystov, V. V., Mykhal'chuk, B. R.   +2 more
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Multilinear Singular and Fractional Integrals

Acta Mathematica Sinica, English Series, 2006
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Ding, Yong, Lu, Shanzhen, Yabuta, Kôzô
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An Integrable Mapping with Fractional Difference

Journal of the Physical Society of Japan, 2003
A generalization of discrete-time Riccati difference equation is introduced. It is shown that this equation has an explicit solution that resembles the discrete form of the Mittag-Leffler function.
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On Fractional Integrals Equivalent to a Constant

Canadian Mathematical Bulletin, 1982
AbstractThe paper is concerned with the Liouville-Riemann and Weyl fractional integrals. Necessary and sufficient conditions are obtained for a function to have a fractional integral which is equivalent to a constant.
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On the Ranges of Certain Fractional Integrals

Canadian Journal of Mathematics, 1972
Suppose 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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