Discretized fractional calculus
SIAM Journal on Mathematical Analysis
A finite difference scheme for partial integro-differential equations with a weakly singular kernel
Applied Numerical Mathematics
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Short memory principle and a predictor-corrector approach for fractional differential equations
Journal of Computational and Applied Mathematics
Discretized Fractional Calculus with a Series of Chebyshev Polynomial
Electronic Notes in Theoretical Computer Science (ENTCS)
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Computational algorithms for computing the fractional derivatives of functions
Mathematics and Computers in Simulation
Numerical algorithm based on Adomian decomposition for fractional differential equations
Computers & Mathematics with Applications
On the fractional Adams method
Computers & Mathematics with Applications
On the stable numerical evaluation of caputo fractional derivatives
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
Computers & Mathematics with Applications
Analytical solution of the linear fractional system of commensurate order
Computers & Mathematics with Applications
New numerical methods for the Riesz space fractional partial differential equations
Computers & Mathematics with Applications
Approximation of fractional integrals by means of derivatives
Computers & Mathematics with Applications
Mixed spline function method for reaction-subdiffusion equations
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
Nowadays, fractional calculus are used to model various different phenomena in nature, but due to the non-local property of the fractional derivative, it still remains a lot of improvements in the present numerical approaches. In this paper, some new numerical approaches based on piecewise interpolation for fractional calculus, and some new improved approaches based on the Simpson method for the fractional differential equations are proposed. We use higher order piecewise interpolation polynomial to approximate the fractional integral and fractional derivatives, and use the Simpson method to design a higher order algorithm for the fractional differential equations. Error analyses and stability analyses are also given, and the numerical results show that these constructed numerical approaches are efficient.