The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator establish some new inequalities for extended Chebyshev functionals. In addition, we investigate positive continuous functions by employing a operator. findings study are theoretical but have potential help solve additional practical problems in mathematical physics, statistics, and appr...

In this paper, we tried to evaluate the fractional derivatives by using the Chebyshev series expansion. We discuss the indefinite quadrature rule to estimate the fractional derivatives of Riemann-Liouville type.

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...

We study two questions associated with rational approximation of a function f(z) near the origin z-0: continuity of the Pad approximation operator, and convergence of Chebyshev to Pad ap-proximants as the domain of approximation shrinks to a point. Both become delicate in the case of degenerate approximations, i.e. approximations whose numerator and denominator are deficient in degree. In this ...

For a broad class of nonlinear regression models we investigate the local Eand c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrema of the equi-oscillating best approximation of the function f0 ≡ 0 by a normalized linear combination of the regression functi...

For a broad class of nonlinear regression models we investigate the local Eand c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrema of the equi-oscillating best approximation of the function f0 ≡ 0 by a normalized linear combination of the regression functi...

Extended Chebyshev spaces that also comprise the constants represent large families of functions that can be used in real-life modeling or engineering applications that also involve important (e.g. transcendental) integral or rational curves and surfaces. Concerning computer aided geometric design, the unique normalized B-bases of such vector spaces ensure optimal shape preserving properties, i...