The fractional Chebyshev collocation method for the numerical solution of fractional differential equations with Riemann-Liouville derivatives
Proceedings of the American Control Conference
The topic of numerical methods for solving fractional differential equations (FDEs) with Riemann-Liouville (RL) derivatives has not received extensive attention compared to the ones for solving FDEs with Caputo derivatives. There is, also, not a sophisticated method to approximate fractional-order derivatives of a function in the sense of RL. In this paper, a new representation of FDEs with fractional-order initial conditions is given, which can be solved in a proposed spectral collocation framework. For this purpose, a new operational matrix of left-sided RL fractional differentiation is constructed to approximate the left-sided RL derivative operator at Chebyshev-Gauss-Lobatto points. In numerical examples, the advantages of using the proposed operational matrix in calculating fractional derivatives of a function or solving FDEs with RL derivatives are illustrated.
Link to Published Version
Dabiri, A., & Karimi, L. (2019). The fractional Chebyshev collocation method for the numerical solution of fractional differential equations with Riemann-Liouville derivatives. 2019 American Control Conference (ACC) , 5493–5498. https://doi.org/10.23919/ACC.2019.8814991