THERMAL SCIENCE
International Scientific Journal
Find this paper on
NUMERICAL ALGORITHM BASED ON FAST CONVOLUTION FOR FRACTIONAL CALCULUS
ABSTRACT
In this paper, numerical algorithms based on fast convolution for the fractional integral and fractional derivative are proposed. Two examples are also included which show the efficiency of the derived method.
KEYWORDS
numerical approach, fractional calculus, fast convolution, Riemann-Liouville derivative, Caputo derivative
PAPER SUBMITTED: 2011-04-07
PAPER REVISED: 2011-07-11
PAPER ACCEPTED: 2011-07-18
DOI REFERENCE: https://doi.org/10.2298/TSCI110407074C
CITATION EXPORT: view in browser or download as text file
REFERENCES
[1] Lubich, C., Schadle, A., Fast convolution for nonreflecting boundary conditions, SIAM J. Sci. Comput., 24 (2002), 1, pp. 161-182
[2] Schadle, A., López-Fernández, M., Lubich, C., Fast and oblivious convolution quadrature, SIAM J. Sci. Comput., 28 (2006), 2, pp. 421-438
[3] López-Fernández, M., Lubich, C., Schädle, A., Adaptive, fast and oblivious convolution in evolution equations with memory, SIAM J. Sci. Comput., 30 (2007), 2, pp. 1015-1037
[4] Li, C. P., Deng, W. H., Remarks on fractional derivatives, Appl. Math. Comput., 187 (2007), 2, pp. 777-784
[5] Diethelm, K., Ford, N. J., Freed, A. D., Luchko, Yu., Algorithms for the fractional calculus: a selection of numerical methods, Comput. Methods Appl. Mech. Eng., 194 (2005), 6-8, pp.743-773
[6] López-Fernández, M., Palencia C., Schädle, A., A spectral order method for inverting sectorial Laplace transforms, Comput. SIAM J. NUMER. ANAL., 44 (2006), 3, pp. 1332-1350
[7] López-Fernández, M., Palencia C., On the numerical inversion of the Laplace transform of certain holomorphic mappings, Appl. Numer. Math., 51 (2004), 2-3, pp. 289-303
[8] Li, C. P., Chen, A., Ye, J. J., Numerical approaches to fractional calculus and fractional ordinary differential equation, J. Comput. Phys., 230 (2011), 9, pp. 3352-3368
[9] Li, C. P., Tao, C. X., On the fractional Adams method, Comput. Math. Appl., 58 (2009), 8, pp. 1573-1588
PDF VERSION [DOWNLOAD]
© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence


