A Novel Operational Matrix Method for Solving the Fractional Delay Integro-Differential Equations with a Weakly Singular Kernel

In this work, we introduce a feasible and efficient method for solving weakly singular fractional pantograph delay integro-differential equations. To implement the proposed method, we get the operational matrices based on the shifted fractional-order fifth-kind Chebyshev polynomials. These matrices, together with the collocation method, are applied to convert the main equation to a system of algebraic equations. We consider the existence and uniqueness of solutions and then give an upper error bound for this method. At last, several numerical tests are carried out to demonstrate the usefulness and capability of the suggested algorithm.