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, ۳۴۱۴۹-۱۶۸۱۸, Iran
Elyas shivanian - Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, ۳۴۱۴۹-۱۶۸۱۸, Iran
Hesam Derili - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

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.

Operational matrices, fractional delay integro-differential equation, Weakly singular kernel