Fermat Operational Matrix for Solving Nonlinear Fractional Differential Equations Using Spectral Galerkin Method
DOI:
https://doi.org/10.31185/wjps.1070Keywords:
Fermat polynomials, Nonlinear Fractional Equations, Fermat operational matrix, Galerkin methodAbstract
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.
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