Operational matrix for multi-order fractional differential equations with hermite polynomials

Year 2024, Volume: 42 Issue: 4, 1050 - 1057, 01.08.2024

Hatice Yalman Koşunalp , Mustafa Gülsu

Abstract

In this article, a new operational matrix of fractional integration of Hermite polynomials is derived to solve multi-order linear fractional differential equations (FDEs) with spectral tau approach. We firstly convert the FDEs into an integrated-form through multiple fractional integration in association with the Riemann-Liouville sense. This integral equation is then formulated as an algebraic equation system with Hermite polynomials. Finally, linear multi-order FDEs with initial conditions are solved with this method. We present exact and approximated solutions for a number of representative examples. Numerical results indicate that the proposed method provides a high degree of accuracy to solve the linear multi-order FDEs.

Keywords

Fractional Differential Equations, Orthogonal Polynomials, Operational Matrix

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