Hafez, Ramy M.Ezz-Eldien, Samer S.Bhrawy, Ali H.Ahmed, Engy A.Baleanu, Dumitru2019-11-302019-11-302015Cited References in Web of Science Core Collection: 560924-090Xhttps://doi.org/10.1007/s11071-015-2250-7https://link.springer.com/article/10.1007/s11071-015-2250-7Accession Number: WOS:000362965700027In this article, we construct a new numerical approach for solving the time-fractional Fokker-Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss-Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss-Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker-Planck equation and the time-space-fractional Fokker-Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm.enUniversity for Collocation methodJacobi polynomialsGauss-Lobatto quadratureGauss-Radau quadratureFractional Fokker-Planck equationCaputo fractional derivativesNUMERICAL-SOLUTIONDIFFERENTIAL-EQUATIONSSPACEAPPROXIMATIONDIFFUSIONCONVERGENCEArticlehttps://doi.org/10.1007/s11071-015-2250-7