New Mittag-Leffler Spectral Method Based on Fractional Chelyshkov Polynomial to Solve Multi-Type of Fractional Ordinary Differential Equations

In this research, a new weighting method was presented based on the truncated fractional Mittag-Leffler function. Alternatives to Jacobi polynomials represented by the Chelyshkov polynomial with the orthogonal property and the fractional degree were relied upon. This approach is based on weighted residual methods. The differential equations are converted into a system of linear or nonlinear algebraic equations. Accurate results were obtained in various applications, and the convergence of the proposed method was studied and the Chelyshkov polynomial was compared with other functions. In addition, weighting methods were compared. In comparison with other methods, the results showed the efficiency of the proposed method in solving such types of fractional equations.