Jacobi spectral collocation method for solving fractional pantograph delay differential equations

In this study, we mainly discuss the application of the Jacobi collocation method to a class of fractional-order pantograph delay differential equations. We first convert the problem to a nonlinear Volterra integral equation with a weakly singular kernel. Under reasonable assumptions of nonlinearity, the existence and uniqueness of the obtained integral equation are derived. Then, we apply a numerical scheme based on the Jacobi collocation approximation to solve the equivalent integral equation. Furthermore, an error analysis for the numerical scheme is performed. Finally, numerical examples are presented to validate our theoretical analysis.