The fractional Chebyshev collocation method for the numerical solution of fractional differential equations with Riemann-Liouville derivatives

Document Type

Conference Proceeding

Publication Date



Engineering Technology

Publication Title

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.

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