University of Guilan Journal of Mathematical Modeling 2345-394X 11 2 2023 07 01 A new approach to solve weakly singular fractional-order delay integro-differential equations using operational matrices 257 275 6207 10.22124/jmm.2023.23316.2080 EN Saeedeh Rezabeyk Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran Saeid Abbasbandy Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran Elyas Shivanian Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran Hesam Derili Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran Journal Article 2022 11 25 In this paper, we propose a new approach to solve weakly singular fractional delay integro-differential equations. In the proposed approach, we apply  the operational matrices of fractional integration and delay function based on the shifted Chebyshev polynomials to approximate the solution of the considered equation. By approximating the fractional derivative of the unknown function as well as the unknown function in terms of the shifted Chebyshev polynomials and substituting these approximations into the original equation, we obtain a system of nonlinear algebraic equations. We present the convergence analysis of the proposed method. Finally, to show the accuracy and validity of the proposed method, we give some numerical examples. https://jmm.guilan.ac.ir/article_6207_f0eddb59636a94b8f6f3a8d3c7515f30.pdf