Fermat Operational Matrix for Solving Nonlinear Fractional Differential Equations Using Spectral Galerkin Method

This paper presents a truncated series of Fermat polynomials as a quick and effective way to solve fractional differential equations numerically. The suggested method converts the fractional differential equation with its beginning conditions into a set of algebraic equations. This transformation is achieved by using the Galerkin spectral technique in conjunction with the matrix of operations for fractional-order derivatives according to Caputo's definition of Fermat polynomials. The precision, efficiency, and stability of the suggested approach are illustrated through a series of numerical examples. The results also show excellent compatibility with exact solutions even when the exact solution is non-polynomial. In addition, comparisons with previously reported methods confirm the higher performance and reliability of the current strategy.