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.

Deflectometry is a non-destructive, full-field phase measuring method, which usually used for inspecting optical specimens with special characteristics, such as highly reflective or specular surfaces, well free-form surfaces. One of the important steps in method to retrieve surface from slope data points on sample map reconstruction. This paper proposes modal reconstruction using an adjustable ...

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...

Cangul-Ozden-Simsek[1] constructed the q-Genocchi numbers of high order using a fermionic p-adic integral on Zp, and gave Witt’s formula and the interpolation functions of these numbers. In this paper, we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers of Cangul-Ozden-Simsek. We define q-extensions of w-Euler numbers and polynomials, and w-Genocchi numbers ...

Some multipoint iterative methods without memory, for approximating simple zeros of functions of one variable, are described. For m > 0, n ≥ 0, and k satisfying m+1 ≥ k > 0, there exist methods which, for each iteration, use one evaluation of f, f ′, . . . , f (m), followed by n evaluations of f (k), and have order of convergence m + 2n + 1. In particular, there are methods of order 2(n+1) whic...

We derive a family of high-order, structure-preserving approximations of the Riemannian exponential map on several matrix manifolds, including the group of unitary matrices, the Grassmannian manifold, and the Stiefel manifold. Our derivation is inspired by the observation that if Ω is a skew-Hermitian matrix and t is a sufficiently small scalar, then there exists a polynomial of degree n in tΩ ...