Baleanu, DumitruGhorbani, Asghar2021-01-292025-09-182021-01-292025-09-182020Ghorbani, Asghar; Baleanu, Dumitru (2020). "Fractional spectral differentiation matrices based on Legendre approximation", Advances in Difference Equations, Vol. 2020, No. 1.1687-1847https://doi.org/10.1186/s13662-020-02590-4https://hdl.handle.net/20.500.12416/10704A simple scheme is proposed for computing NxN spectral differentiation matrices of fractional order alpha for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous three-term recurrence relation and is numerically stable. The matrices are then applied to numerically differentiate.eninfo:eu-repo/semantics/openAccessFractional Spectral Differentiation MatricesFractional CalculusLegendre PolynomialsNumerical DifferentiationArticle10.1186/s13662-020-02590-42-s2.0-85082579459