An accurate operational matrix method based on Lagrange polynomials for solving fractional-order pantograph delay and Riccati differential equations

This paper introduces the fractional-order Lagrange polynomials approach to solve initial value problems for pantograph delay and Riccati differential equations involving fractional-order derivatives. The fractional derivative is determined as per the idea of Caputo. First, operational matrices of fractional integration with fractional-order Lagrange polynomials have been constructed using the Laplace transform. Then, we use these operational matrices and the collocation method to convert the given initial value problem to a system of algebraic equations. Subsequently, we use Newton's iterative approach to solve the resultant system of algebraic equations. Error estimates for the function approximation also have been discussed. Finally, some numerical examples supported the theoretical findings by demonstrating the applicability and accuracy of the proposed strategy.