Nonlinear fractional differential equations reflect the true nature of physical and biological models with non-locality memory effects. This paper considers nonlinear unknown analytical solutions. The Adomian decomposition power series methods are adopted to approximate two approaches illustrated compared by means four numerical examples.

The aim of this article is by using the fractional complex transform FCT and the optimal homotopy analysis transform method OHATM to find the analytical approximate solutions for nonlinear fractional differential-difference equations FNDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. Fractional complex transform...

We study the functional link between the Hurst parameter and the normalized total wavelet entropy when analyzing fractional Brownian motion (fBm) time series—these series are synthetically generated. Both quantifiers are mainly used to identify fractional Brownian motion processes [L. Zunino, D.G. Pérez, M. Garavaglia, O.A. Rosso, Characterization of laser propagation through turbulent media by...

Consider the fractional ARIMA time series with innovations that have innnite variance. This is a nite parameter model which exhibits both long-range dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Kl uppelber...

The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox-Wright functions. A series expansion is also provided in order to point out the distribution of time-scales r...

Rare earth abundances were determined by neutron activation in twenty Hawaiian lavas and one diabase of known chemical and mineralogical compositions. These results demonstrate a systematic relationship between the absolute or relative rare earth abundances and the petroehemistry of these rocks. Three distinct lava groups are recognized. These correspond to: (1) tholeiites, (2) alkali series, (...

This paper extends previous analyses of aggregate political popularity (partisanship) data by BoxSteffensmeier and Smith (1996) for the US, and Byers, Davidson and Peel (1997) for the UK. These studies independently found that the time series of poll ratings are well modelled by fractionally integrated processes. Here, the analysis is conducted for 26 political parties in eight different countr...

We introduce a concept of a fractional derivatives series and prove that any linear partial differential equation in two independent variables has a fractional derivatives series solution with coefficients from a differentially closed field of zero characteristic. The obtained results are extended from a single equation to D-modules having infinitedimensional space of solutions (i.e., non-holon...

In this article, we present a fractional order HIV-1 infection model of CD4+ T-cell. We analyze the effect of the changing the average number of the viral particle N with initial conditions of the presented model. The Laplace Adomian decomposition method is applying to check the analytical solution of the problem. We obtain the solutions of the fractional order HIV-1 model in the form of infini...