Numerical solution of fractional integro-differential equation by collocation Pell-Lucas polynomial method

Abstract

The objective of this work is to solve the fractional integro-differential equation using the Pell-Lucas collocation method. In this approach, the fractional derivative is considered in the Caputo sense. The proposed approach for dealing with the problem is the collocation method based on the Pell-Lucas polynomials to obtain an approximation of the solution. The operational matrix of the Caputo derivative, based on the Pell-Lucas polynomials, is derived and utilized in the solution process. By discretizing the Fredholm integral term and the corresponding conditions in terms of the Pell-Lucas polynomials, the original problem is transformed into a system of algebraic equations, which can be solved numerically. The error analysis has been investigated and error estimation of the Pell-Lucas collocation method is studied for the considered problem. Some illustrative examples are investigated to show the accuracy and applicability of the proposed method.