What is it about?
Fractional-order ordinary differential equations (FODEs) may be solved numerically using the infinite state representation which transforms the FODE to an approximating high-dimensional ODE. This paper introduces a reformulation of the infinite state representation, which leads to a better convergence behaviour of the related numerical scheme.
Featured Image
Why is it important?
We introduce a new representation of the fractional derivative which includes improper integrals with integrable kernels, whereas the classical infinite state representation contains weakly singular integration kernels. Thus, the numerical method using the reformulated representation shows a better performance in several benchmark problems than classical schemes.
Perspectives
The reformulated infinite state representation was originally developed to prove stability of fractionally damped mechanical systems with the help of Lyapunov functionals. Our article relates this rather theoretical topic to the numerical solution of FODEs, which is an important task in many applications. Hence, I hope to provide a good example in linking theoretical and applied investigation.
Matthias Hinze
Universitat Stuttgart
Read the Original
This page is a summary of: Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation, Fractional Calculus and Applied Analysis, October 2019, De Gruyter,
DOI: 10.1515/fca-2019-0070.
You can read the full text:
Contributors
The following have contributed to this page
