Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
Journal of Approximation Theory
Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials
Journal of Scientific Computing
Short memory principle and a predictor-corrector approach for fractional differential equations
Journal of Computational and Applied Mathematics
Numerical algorithm for the time fractional Fokker-Planck equation
Journal of Computational Physics
Spectral Methods: Algorithms, Analysis and Applications
Spectral Methods: Algorithms, Analysis and Applications
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We present a novel predictor-corrector method, called Jacobian-predictor-corrector approach, for the numerical solutions of fractional ordinary differential equations, which are based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t. the Jacobi-weight function $\omega (s)=(1-s)^{\alpha -1} (1+s)^{0}$. This method has the computational cost O(NE) and the convergent order NI, where NE and NI are, respectively, the total computational steps and the number of used interpolation points. The detailed error analysis is performed, and the extensive numerical experiments confirm the theoretical results and show the robustness of this method.