New explicit and accelerated techniques for solving fractional order differential equations
作者：
Highlights：
• The Caputo fractional numerical differentiation is directly built from the original FDE so that the discrete formula for the solution has an explicit form.
• The numerical formula for the Caputo fractional derivative is not involved by the derivative of y(t) so that a simple linear interpolate approximation can be easily applied.
• For a fractional order ν ≈ 0, the stable perturbation technique is proposed compared with other methods.
• Numerical performance can be boosted up by the technique of the decomposition of ν in case of that ν ≈ 1.
摘要
•The Caputo fractional numerical differentiation is directly built from the original FDE so that the discrete formula for the solution has an explicit form.•The numerical formula for the Caputo fractional derivative is not involved by the derivative of y(t) so that a simple linear interpolate approximation can be easily applied.•For a fractional order ν ≈ 0, the stable perturbation technique is proposed compared with other methods.•Numerical performance can be boosted up by the technique of the decomposition of ν in case of that ν ≈ 1.
论文关键词：Caputo fractional derivative,Fractional differential equations,Predictor-corrector methods,Explicit scheme,High-order method
论文评审过程：Received 5 July 2019, Revised 25 February 2020, Accepted 15 March 2020, Available online 13 April 2020, Version of Record 13 April 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125228
