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...

Cone polynomials in n > 1 variables, also known as volume polynomials and/or spline polynomials, are the polynomials that appear in the local structure of the truncated powers, hence in the local structure of any derived construction such as box splines, simplex splines, partition functions, character formulas and moment maps. The underlying geometry is determined by a real linear matroid, i.e....

We discuss the properties of the truncated exponential polynomials and develop the theory of new form of Hermite polynomials, which can be constructed using the truncated exponential as a generating function. We derive their explicit forms and comment on their usefulness in applications, with particular reference to the theory of flattened beams, used in optics.

In this paper, we present a Taylor-series expansion method for a class of Fredholm singular integro-differential equation with Cauchy kernel. This method uses the truncated Taylor-series polynomial of the unknown function and transforms the integro-differential equation into an nth order linear ordinary differential equa.tion with variable coefficients: ~y Galerkin method we use the orthogonal ...

The aim of the study is to develop a numerical method for solution cubic nonlinear differential equations in which based on Boole polynomials. That form truncated series and gives approximate type. In this method, firstly, matrix serial set equation converted into system. By adding effect both conditions problem collocation points system equations, we obtain new equations. coefficients Boole-ba...

in the present study, the onset of double diffusive reaction-convection in a uid layer with viscous fluid, heated and salted from below subject to chemical equilibrium on the boundaries, has been investigated. linear and nonlinear stability analysis have been performed. for linear analysis normal mode technique is used and for nonlinear analysis minimal representation of truncated fourier serie...

Knowledge of a truncated Fourier series expansion for a discontinuous 2^-periodic function, or a truncated Chebyshev series expansion for a discontinuous nonperiodic function defined on the interval [-1, 1], is used in this paper to accurately and efficiently reconstruct the corresponding discontinuous function. First an algebraic equation of degree M for the M locations of discontinuities in e...

We consider the explicit relation between two resolvent matrices related to truncated Hausdorff matrix moment problem (THMM) in case of an even and odd number moments. This is described with help four families orthogonal polynomials on finite interval [a, b] their associated second kind polynomials.