In this paper, we tried to evaluate the fractional derivatives by using the Chebyshev series expansion. We discuss the indefinite quadrature rule to estimate the fractional derivatives of Riemann-Liouville type.

We study polynomial identities of algebras with involution nonassociative over a field characteristic zero. prove that the growth sequence ⁎-codimensions finite-dimensional algebra is exponentially bounded. construct series fractional ⁎-PI-exponent. also family infinite-dimensional Cα such exp⁎(Cα) does not exist.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fraction...

The response of lowpass maximally flat digital filters to polynomial signals is analyzed by means of a formal algebraic method in the z domain. The general class of maximally flat FIR filters, encompassing linear-phase, non-linear-phase, and half-band filters, is studied. A characterization of polynomial signals in the z domain is introduced, and it is shown that for a given member of the class...

A numerical technique for Volterra functional integral equations (VFIEs) with non-vanishing delays and fractional Bagley-Torvik equation is displayed in this work. The depends on Bernstein polynomial approximation. Numerical examples are utilized to evaluate the accurate results. findings figs tables show that simple use.

| We study fairness when receivers in a multi-cast network can not subscribe to fractional layers. This case arises when the source hierarchically encodes its signal and the hierarchical structure is predetermined. Unlike the case of the fractional layer allocation, which has been studied extensively in 14], bandwidth can be allocated in discrete chunks only. Fairness issues become vastly diier...

We study fairness when receivers in a multicast network can not subscribe to fractional layers. This case arises when the source hierarchically encodes its signal and the hierarchical structure is predetermined. Unlike the case of the fractional layer allocation, which has been studied extensively in [29], bandwidth can be allocated in discrete chunks only. Fairness issues become vastly differe...

Matching 2-lattice polyhedra are a special class of lattice polyhedra that include network 3ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, etc. In this paper we develop a polynomial-time extreme point algorithm for #nding a maximum cardinality vector in a matching 2-lattice polyhedron. c © 2001 Elsevier Science B.V. All rights reserved.

Based on an idea of Granger (1986), we analyze a new vector autoregressive model de…ned from the fractional lag operator 1 (1 L)d: We …rst derive conditions in terms of the coe¢ cients for the model to generate processes which are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process Xt of order d; d > 0; for which there are vectors so tha...