Chebyshev polynomials of the first and the second kind in n variables z. , Zt , ... , z„ are introduced. The variables z, , z-,..... z„ are the characters of the representations of SL(n + 1, C) corresponding to the fundamental weights. The Chebyshev polynomials are eigenpolynomials of a second order linear partial differential operator which is in fact the radial part of the Laplace-Beltrami op...

We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the pap...

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...

In this paper, the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linearly stretching sheet is solved using the combination of the quasilinearization method and the Fractional order of Rational Chebyshev function (FRC) collocation method on a semi-infinite domain. The quasilinearization method converts the equation into a sequence of linear equations then, using the FRC coll...

A common practice for computing an elementary transcendental function nowadays has two phases: reductions of input arguments to fall into a tiny interval and polynomial approximations for the function within the interval. Typically the interval is made tiny enough so that one won’t have to go for polynomials of very high degrees for accurate approximations. Often approximating polynomials as su...

In the present paper we prove the Chebyshev inequality involving two isotonic linear functionals. Namely, if A and B are isotonic linear functionals, then A(p f g)B(q)+A(p)B(q f g) A(p f )B(qg) + A(pg)B(q f ) , where p,q are non-negative weights and f ,g are similarly ordered functions such that the above-mentioned terms are well-defined. If functionals are equal, i.e. A = B and if p = q , then...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

in this paper, some results of the chebyshev type integral inequality for the pseudo-integral are proven. the obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. finally, we applied our results  to the case of comonotone functions.