The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Algorithms for the fractional calculus: A selection of numerical methods
Open accessAbstract
Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.
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Cites
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Owen, D. B., Abramowitz, M., & Stegun, I. A. (1965) · Technometrics · doi:10.2307/1266136 · Cited by 16,138
An Introduction to the Fractional Calculus and Fractional Differential Equations
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Fractional Integrals and Derivatives, Theory and Applications
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A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations
Diethelm, K., Ford, N. J., & Freed, A. D. (2002) · Nonlinear Dynamics · doi:10.1023/a:1016592219341 · Cited by 2,557
Self-citation(1964) · doi:10.1115/1.3625776 · Cited by 1,796
Creep Problems in Structural Members
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Detailed Error Analysis for a Fractional Adams Method
Diethelm, K., Ford, N. J., & Freed, A. D. (2004) · Numerical Algorithms · doi:10.1023/b:numa.0000027736.85078.be · Cited by 1,029
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Cited by
On Riemann and Caputo fractional differences
Abdeljawad, T. (2011) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2011.03.036 · Cited by 733
Two-scale mechanism-based theory of nonlinear viscoelasticity
Tang, S., Steven Greene, M., & Liu, W. K. (2012) · Journal of the Mechanics and Physics of Solids · doi:10.1016/j.jmps.2011.11.003 · Cited by 87
Effects of frequency-dependent membrane capacitance on neural excitability
Howell, B., Medina, L. E., & Grill, W. M. (2015) · Journal of Neural Engineering · doi:10.1088/1741-2560/12/5/056015 · Cited by 39
Metadata
- Authors
- Diethelm, K., Ford, N. J., Freed, A. D., & Luchko, Y.
- Venue
- Computer Methods in Applied Mechanics and Engineering
- Publisher
- Elsevier BV
- Published
- 2005-02
- Volume
- 194
- Issue
- 6-8
- Pages
- 743-773
- ISSN
- 0045-7825 (ISSN-L)
- OpenAlex
- W1993680495
- Cited by
- 684
- References
- 21
- FWCI
- 13.93
- Type
- journal article
- Language
- en
- Open access
- green
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