This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with d < 1, which implies mean reversion. The multivariate framework exploiting recent developments in fr...

This guide to the neurological disorder cerebral autosomal dominant arteriopathy with subcortical infarcts and leuco encephalopathy (CADASIL) is specifically targeted at psychiatrists. The aims are to enhance awareness, provide educational clinical information and offer practical guidance on management of the disorder. An overview of diagnostic algorithms and recent research is also provided. M...

In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with timevarying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative o...

In this paper, a collocation method based on the Bernstein polynomials is presented for the fractional Riccati type differential equations. By writing t? ta (0 < a < 1) in the truncated Bernstein series, the truncated fractional Bernstein series is obtained and then it is transformed into the matrix form. By using Caputo fractional derivative, the matrix forms of the fractional derivatives are ...

The fractional polylogarithms, depending on a complex parameter α, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional polylogarithms are multivalued analytic functions in the complex plane minus 0 and 1. For non-integer values of α, we prove the analytic continuation, compute the...

The fundamental concern of this article has been to apply the residual power series method (RPSM) effectively to determine of the unknown spacewise dependent coefficient in the time fractional heat equation in the Caputo sense with over measured data. First, the fractional power series solution of inverse problem of unknown spacewise dependent coefficient is obtained by residual power series me...

Fractional Brownian Motions (FBM) are selfsimilar Gaussian processes with hölder-continuous paths, that can be represented as fractional integrals (H > 12) or derivatives (H < 1 2) of Brownian Motions (BM), allow an stochastic calculus, have long-range memory and are of interest in finance and network traffic. For the theory and for the numerical simulation of FBM series expansions are of inter...

In this note we consider colorings of series-parallel graphs. Specifically, we provide bounds on their fractional and circular chromatic numbers and the defective version of these parameters. The main result is that the fractional chromatic number of any series-parallel graph of odd girth k is exactly 2k/(k − 1).