Results 271 to 280 of about 1,361,829 (303)

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
openaire   +1 more source

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
openaire   +2 more sources

A Note on the Fractional Integrated Fractional Brownian Motion

Acta Applicandae Mathematica, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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 ...
openaire   +1 more source

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
openaire   +1 more source

Multilinear Singular and Fractional Integrals

Acta Mathematica Sinica, English Series, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Yong, Lu, Shanzhen, Yabuta, Kôzô
openaire   +1 more source

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.
openaire   +2 more sources

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.
openaire   +1 more source

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-
openaire   +2 more sources

Fractional Integration

American Journal of Mathematics, 1953
openaire   +1 more source