A New Method for Solving The Fractional Spectral Collocation Equation

Maryam Aad  Alwan; Hayder Hassoon Mohammed

Maryam Aad Alwan Ministry of Education, Najaf Education Directorate, Iran
Hayder Hassoon Mohammed Ministry of Education, Najaf Education Directorate, Iran

Keywords: Fractional Partial Differential Equations, Collision Spectral Method, Fractional Lagrange Interpolators, Exponential Convergence, Borgers Equation And Fokker-Planck Equation

Abstract

This research presents a fractional discrete collision spectral method (FSCM) for solving fractional-order partial differential equations (FPDEs) such as the Borgers equation and the Fokker-Planck equation. The method is based on constructing exact fractional numerical derivatives using a fractional Lagrange interpolator that satisfies the Kronecker delta property at collision points. Fractional PDEs are developed based on several proposed points, including the roots of fractional Jacobian polynomials, achieving exponential convergence in solutions. The study includes an analysis of numerical matrices of fractional derivatives and a comparison of applications in multiple time-invariant and constant-time problems. The method is characterized by ease of implementation and reduced computational cost compared to traditional methods.

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