Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations

Abstract

A new class of polynomials investigates the numerical solution of the fractional pantograph delay ordinary differential equations. These polynomials are equipped with an auxiliary unknown parameter $a$ , which is obtained using the collocation and least-squares methods. In this study, the numerical solution of the fractional pantograph delay differential equation is displayed in the truncated series form. The upper bound of the solution as well as the error analysis and the rate of convergence theorem are also investigated in this study. In five examples, the numerical results of the present method have been compared with other methods. For the first time, $a$ -polynomials are used in this study to numerically solve delay equations, and accurate approximations have been displayed.