TY - JOUR ID - 9655 TI - The solving integro-differential equations of fractional order with the ultraspherical functions JO - Computational Methods for Differential Equations JA - CMDE LA - en SN - 2345-3982 AU - Khani, Ali AU - Panahy, Saeid AD - Faculty of Sciences, Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran AD - Facutly of Sciences Department of Mathematical , Azarbaijan Shahid Madani University, Tabriz, Iran Y1 - 2020 PY - 2020 VL - 8 IS - 1 SP - 205 EP - 211 KW - Fractional integro-differential equation KW - Ultraspherical functions KW - Caputo derivative DO - 10.22034/cmde.2019.9655 N2 - 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. UR - https://cmde.tabrizu.ac.ir/article_9655.html L1 - https://cmde.tabrizu.ac.ir/article_9655_4fadc94c41f9800d90c3f50c47193d78.pdf ER -