An efficient method for linear fractional delay integro-differential equations

In this paper, we focus on an efficient convergent method to solve the linear fractional delay integro-differential equations. We first convert the equation into an equivalent system by replacing the delay function in the sections containing delay in two intervals before the delay time and after the delay time. In the next step, we discretize the new gain system at the Jacobi–Gauss collocation points and acquire a system of algebraic equations to approximate the solution. Here, we simultaneously obtain the solution and its derivative of fractional order. We exhibit the convergence analysis of approximate solution to the exact solution in L ω α , β ∞ ( I ) -space, and finally with several numerical examples, we show the capability of the method.