Numerical solution of nonlinear fractional delay integro-differential equations with convergence analysis

In this work, a high accurate method is given for solving the nonlinear fractional delay integro-differential equations, numerically. By considering the equation before and after delay time, we first apply the delay function in the equation and propose an equivalent system. By discretization in the Jacobi-Gauss collocation points, an algebraic nonlinear system is then proposed to approximate the solution of main equation. The convergence of method is fully given in spaces \(L^{\infty }_{\omega ^{\alpha ,\beta }}(I)\) $L_{{\omega }^{\alpha ,\beta }}^{\infty }(I)$ and \(L^{2}_{\omega ^{\alpha ,\beta }}(I)\) $L_{{\omega }^{\alpha ,\beta }}^2(I)$ , and the error bounds are specified for obtained approximations. Finally, some numerical examples are provided to show the capability and efficiency of method.