In this paper, the Chebyshev-I conformable differential equation is considered. A proper power series examined; there are two solutions, even solution and odd solution. The Rodrigues’ type formula also allocated for polynomials.

In this paper, we propose the cubic semi-orthogonal compactly supported B-spline wavelets as a basis functions for the efficient solution of the second kind Fredholm integral equations system. Properties of these wavelets first presented and these properties are then used to reduce the computation of system of integral equations to some algebraic equations. The exponential convergence rate of t...

A simple strategy for constructing a sequence of increasingly refined interpolation grids over the triangle or the tetrahedron is discussed with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The interpolation nodes are generated based on a one-dimensional master grid comprised of the zeros of the Lobatto, Legendre, Chebyshev, and second-kind Chebyshev polyn...

We study the regularity of form ( linear functional) satisfying functional equation (x2 ? c2)u = ?v where c C, C {0} and v is perturbed order one Chebyshev second kind. The integral representation u highlighted. Moreover, some symmetric degree forms class two four are given.

with given a, b, t0, t1 and n ≥ 0. This sequence was introduced by Horadam [3] in 1965, and it generalizes many sequences (see [1, 4]). Examples of such sequences are Fibonacci polynomials sequence (Fn(x))n≥0, Lucas polynomials sequence (Ln(x))n≥0, and Pell polynomials sequence (Pn(x))n≥0, when one has a = x, b = t1 = 1, t0 = 0; a = t1 = x, b = 1, t0 = 2; and a = 2x, b = t1 = 1, t0 = 0; respect...

In this paper, We use the wavelet bases of Hermite cubic splines to solve the second kind integral equations xCi) -11 K(t,s)x(s)ds = y(t), t E [0,1]. A pair of wavelets are constructed on the basis of Hermite cubic spline~: This wavelets are in C1 and supported on [0,2]. Moreover, one wavelet is symmetric, and the other is anti-symmetric. This spline wavelets are then adapted to the interval [0...