A numerical method to solve fractional pantograph differential equations with residual error analysis

Abstract

In this study, we have introduced a fractional series solution method to solve fractional pantograph differential equations numerically. The method is constructed by collocation approach and Bernstein polynomials. Each term of the equation is converted into a matrix form by the fractional Bernstein series. Then, the problems are reduced into a set of algebraic equations including unknown Bernstein coefficients by using the collocation nodes. Hence, by determining the coefficients, the approximate solution is obtained. For the error analysis of this method, we give two techniques which estimate or bound the absolute error. To demonstrate the efficiency and applicability of the method, some illustrative examples are given. We also compare the method with some known methods in the literature.