This paper deals with Chebyshev wavelets. We analyze their properties computing Fourier transform. Moreover, we discuss the differential of wavelets due to connection coefficients. Uniform convergence and approximation error allow us provide rigorous proofs. In particular, expand mother wavelet in Taylor series an application both fractional calculus fractal geometry. Finally, give two examples...

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by...

Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat'...