Abstract
In this paper, we propose a novel approach for the numerical solution of fractional-order ordinary differential equations. The method is based on the infinite state representation of the Caputo fractional differential operator, in which the entire history of the state of the system is considered for correct initialization. The infinite state representation contains an improper integral with respect to frequency, expressing the history dependence of the fractional derivative. The integral generally has a weakly singular kernel, which may lead to problems in numerical computations. A reformulation of the integral generates a kernel that decays to zero at both ends of the integration interval leading to better convergence properties of the related numerical scheme. We compare our method to other schemes by considering several benchmark problems.
Acknowledgements
This work is supported by the Federal Ministry of Education and Research of Germany under Grant No. 01IS17096.
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© 2019 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–Volume 22–5–2019)
- Survey Paper
- A survey on fractional asymptotic expansion method: A forgotten theory
- Simplified fractional-order design of a MIMO robust controller
- Research Paper
- Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets
- Weyl integrals on weighted spaces
- On fractional regularity of distributions of functions in Gaussian random variables
- Compactness criteria for fractional integral operators
- Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type
- Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications
- Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation
- Supercritical fractional Kirchhoff type problems
- Identification for control of suspended objects in non-Newtonian fluids
- Algebraic fractional order differentiator based on the pseudo-state space representation
- Eigenvalues for a combination between local and nonlocal p-Laplacians
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–Volume 22–5–2019)
- Survey Paper
- A survey on fractional asymptotic expansion method: A forgotten theory
- Simplified fractional-order design of a MIMO robust controller
- Research Paper
- Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets
- Weyl integrals on weighted spaces
- On fractional regularity of distributions of functions in Gaussian random variables
- Compactness criteria for fractional integral operators
- Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type
- Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications
- Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation
- Supercritical fractional Kirchhoff type problems
- Identification for control of suspended objects in non-Newtonian fluids
- Algebraic fractional order differentiator based on the pseudo-state space representation
- Eigenvalues for a combination between local and nonlocal p-Laplacians