In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

In this work, we consider variable order difusion and wave equations. The derivative is describedin the Caputo sence of variable order. We use the Genocchi polynomials as basic functions andobtain operational matrices via these polynomials. These matrices and collocation method help usto convert variable order diusion and wave equations to an algebraic system. Some examples aregiven to show the...

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.

in order to estimate the genetic parameters and comparison legendre polynomials for production traits of iranian holstein dairy cattle test-day records of first lactation cows for milk yield, fat yield, protein yield, fat percentage and protein percentage traits were used. these records collected from 2006 to 2010, by the animal breeding center of iran. the genetic parameters were estimated usi...

in this study test-day records of milk (kg), fat (g), and protein (g) yields, somatic cell score (scs, cells/ml) collected by animal breeding center of iran during 2007 and 2009 were used to estimate genetic parameters using random regression model. models with different order of legendre polynomials were compared using bayesian information criterion (bic).for milk, fat yield and scs genetic an...