A new approach to solve weakly singular fractional-order delay integro-differential equations using operational matrices

Document Type : Research Article


1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

2 Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, 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.