A Matrix Approach by Convolved Fermat Polynomials for Solving the Fractional Burgers’ Equation - Waleed Mohamed Abd-Elhameed; Omar Mazen Alqubori; Naher Mohammed A. Alsafri; Amr Kamel Amin; Ahmed Gamal Atta (Mathematics)
This article employs certain polynomials that generalize standard Fermat polynomials, called convolved Fermat polynomials, to numerically solve the fractional Burgers’ equation. New theoretical results of these polynomials are developed and utilized along with the collocation method to find approximate solutions of the fractional Burgers’ equation. The basic idea behind the proposed numerical algorithm is based on establishing the operational matrices of derivatives of both integer and fractional derivatives of the convolved Fermat polynomials that help to convert the equation governed by its underlying conditions into an algebraic system of equations that can be treated numerically. A comprehensive study is performed to analyze the error of the proposed convolved Fermat expansion. Some numerical examples are presented to test our proposed numerical algorithm, and some comparisons are made. The results indicate that the proposed algorithm is applicable and accurate.