The solving integro-differential equations of fractional order with the ultraspherical functions

Khani, Ali; Panahy, Saeid

doi:10.22034/cmde.2019.9655

The solving integro-differential equations of fractional order with the ultraspherical functions

Document Type : Research Paper

Authors

Ali Khani ¹
Saeid Panahy ²

¹ Faculty of Sciences, Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

² Facutly of Sciences Department of Mathematical , Azarbaijan Shahid Madani University, Tabriz, Iran

10.22034/cmde.2019.9655

Abstract

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.

Keywords