%0 Journal Article
%T The solving integro-differential equations of fractional order with the ultraspherical functions
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Khani, Ali
%A Panahy, Saeid
%D 2020
%\ 01/01/2020
%V 8
%N 1
%P 205-211
%! The solving integro-differential equations of fractional order with the ultraspherical functions
%K Fractional integro-differential equation
%K Ultraspherical functions
%K Caputo derivative
%R 10.22034/cmde.2019.9655
%X In this paper, an integration method is presented based on using ultraspherical polynomials for solving a class of linear fractional integro-di_erential equations of Volterra types. This method is based on a new investigation of ultrasphreical integration to approximate the highest order derivative in the equations and generate approximations to the lower order derivatives through integration of the higher-order derivatives. Numerical example illustrate the efficiency and accuracy of the method.
%U https://cmde.tabrizu.ac.ir/article_9655_4fadc94c41f9800d90c3f50c47193d78.pdf