Hyperbolic decay time series such as, fractional Gaussian noise (FGN) or fractional autoregressive moving-average (FARMA) process, each exhibit two distinct types of behaviour: strong persistence or antipersistence. Beran (1994) characterized the family of strongly persistent time series. A more general family of hyperbolic decay time series is introduced and its basic properties are characteri...

Hyperbolic decay time series such as fractional Gaussian noise or fractional autoregressive moving-average processes exhibit two distinct types of behaviour: strong persistence or antipersistence. Beran (Statistics for Long Memory Processes. London: Chapman and Hall, 1994) characterized the family of strongly persistent time series. A more general family of hyperbolic decay time series is intro...

in this article, we present a fractional order hiv-1 infectionmodel of cd4+ t-cell. we analyze the effect of the changing the averagenumber of the viral particle n with initial conditions of the presentedmodel. the laplace adomian decomposition method is applying to checkthe analytical solution of the problem. we obtain the solutions of thefractional order hiv-1 model in the form of infinite se...

We obtain a new decomposition of the Riemann–Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class Cn, n ∈ N, and allow us to develop suitable numerical approximations with known estimations for the error. The usefulness of the obtained results, in solving fractional integral equations and fractional...

One-dimensional Ginzburg–Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg–Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order α wit...

The modelling of rainfall and other hydrological data has been the point of much discussion in past research. Hurst (1951) heuristically detected the presence of long range dependence (or long memory) in the well-known series of annual minima of the Nile River. These processes are so called because they display a high degree of association between observations which are distant in time. Followi...

In this paper, a comparative study of Picard method, Adomian method and Predictor-Corrector method are presented for fractional integral equation. In Picard method [6] a uniform convergent solution for the fractional integral equation is obtained. Also, for Adomian method, we construct a series solution see ([1], [5] and [7]). Finally, Predictor-Corrector method is used for solving fractional i...

This paper describes some of the results in [5] for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals are defined with explicit expressions for their first two moments. Multiple and iterated integrals of a fractional Browinian motion are defined and various properties of these integrals are given. A square integrab...

Series expansion methods for fractional integrals are important and useful for treating certain problems of pure and applied mathematics. The aim of the present investigation is to obtain certain new fractional calculus formulae, which involve Srivastava polynomials. Several special cases of our main findings which are also believed to be new have been given. For the sake of illustration, we po...

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of comp...