منابع مشابه
Fractional Calculus in NMR
Nuclear magnetic resonance (NMR) is a physical phenomenon widely used to study complex materials. NMR is governed by the Bloch equation, a first order non-linear differential equation. Fractional order generalization of the Bloch equation provides an opportunity to extend its use to describe a wider range of experimental situations. Here we present a fractional generalization of the Bloch equat...
متن کاملOn certain fractional calculus operators involving generalized Mittag-Leffler function
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...
متن کاملFitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data
As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet ...
متن کاملFractional vector calculus for fractional advection–dispersion
We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection–dispersion equation for flow in heterogeneous porous media. r 2005 Elsevier B.V. All rights reserved.
متن کاملFractional vector calculus and fractional Maxwell’s equations
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Alexandria Engineering Journal
سال: 2020
ISSN: 1110-0168
DOI: 10.1016/j.aej.2020.09.002