Algorithms for the fractional calculus: A selection of numerical methods
By Kai Diethelm, Neville J. Ford, Alan D. Freed, Yury F. Luchko. 2005
704 citations recorded by the source corpus.
Subfields: Biomedical Engineering, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/25d5add06f15cdbb7c6affa9c64543d6e7e4c694
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Biomedical Engineering
- Yangang Chen
- G. Diaz
- A. Sami Bataineh
- Mehdi Dehghan
- Dr. T. K. Battula
- Ishak Hashim
- Caibin Zeng
- Carlos F. M. Coimbra
In Modeling and Simulation
- Mehdi Dehghan
- Abbas Saadatmandi
- Changpin Li
- Jafar Saberi-Nadjafi
- M. Izadkhah
- Ali H. Bhrawy
- Weihua Deng
- Dumitru Băleanu
In Numerical Analysis
- Mehdi Dehghan
- Abbas Saadatmandi
- Jafar Saberi-Nadjafi
- M. Izadkhah
- Ali H. Bhrawy
- Changpin Li
- Dumitru Băleanu
- Igor Podlubny
Citations in the corpus
- A CHEBYSHEV PSEUDO-SPECTRAL METHOD FOR SOLVING FRACTIONAL-ORDER INTEGRO-DIFFERENTIAL EQUATIONS (2010, neutral): “Recently, several numerical methods to solve fractional differential equations (FDEs) and fractional integro-differential equations (FIDEs) have been given [ 2, 4, 6, 8–10, 12, 14–25 ] .”
- Global Padé Approximations of the Generalized Mittag-Leffler Function and its Inverse (2013, background): “[3] provided a table of coefficients of the rational approximants to the function Eα(−t) for 0 < α < 1.”
- A Legendre collocation method for fractional integro-differential equations (2011, positive): “For the Caputo’s derivative we have (Diethelm et al., 2005) D C ¼ 0, (C is a constant), ð8Þ D x ¼ 0, for 2 N0 and 5 d e, ð þ1Þ ð þ1 Þx , for 2 N0 and d e or =2N and 4 b c: 8 : ð9Þ We use the ceiling function dae to denote the smallest integer greater than or equal to a, and the floor function bac…”
- Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations (2009, neutral): “the sake of space, since [11] provides a full description of each algorithm.”
- Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative (2007, background): “It should be pointed out here that according to Diethelm et al. (2005), the LCFD had already been introduced in a 19th century paper by Liouville and in a paper by Rabotnov a year prior to the publication of Caputo’s paper.”
- Weyl and Marchaud Derivatives: A Forgotten History (2017, background): “Among them we point out [21] and the recent handbook [37].”
- Numerical solution of the Bagley–Torvik equation by the Bessel collocation method (2013, neutral): “For the Caputo derivative we have [35] D ̨ cD 0, .”