‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

We introduce Chebyshev measures. We generalize the representation theorem concerning both measures admitting a density function which is a T {system and oriented measures.

In this talk, we are concerned with embedded formulae of the Chebyshev collocation methods [1] developed recently. We introduce two Chebyshev collocation methods based on generalized Chebyshev interpolation polynomials [2], which are used to make an automatic integration method. We apply an elegant algorithm of generalized Chebyshev interpolation increasing the node points to make an error esti...

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...

A form of this was conjectured by Gauss about 1800, [Chebyshev 1848/52] and [Chebyshev 1850/52] made notable progress with essentially elementary methods. The landmark paper Riemann 1859] made clear the intimate connection between prime numbers and the behavior of ζ(s) as a function of a complex variable. The theorem was proven independently by [Hadamard 1896] and [de la Vallée Poussin 1896] by...

In this paper we study the number of limit cycles bifurcating from isochronous surfaces of revolution contained in R, when we consider polynomial perturbations of arbitrary degree. The method for studying these limit cycles is based in the averaging theory and in the properties of Chebyshev systems. We present a new result on averaging theory and generalitzations of some classical Chebyshev sys...