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Title: | On a numerical scheme for solving differential equations of fractional order | Authors: | Atanackovic T. Stankovic B. |
Issue Date: | 1-Oct-2008 | Journal: | Mechanics Research Communications | Abstract: | In this work, on the basis of a modified expansion formula obtained in Atanackovic and Stankovic [Atanackovic, T.M., Stankovic, B., 2004. An Expansion formula for fractional derivatives and its applications. Fractional Calculus and Applied Analysis 7(3), 365-378], we propose a numerical procedure for solving differential equations with fractional derivative by transforming the original system into a system of ordinary differential equations of the first order. Our method is different from the widely used method of Yuan and Agarwal [Yuan, L., Agrawal, O. P., 2002. A numerical scheme for dynamic systems containing fractional derivatives. Journal of Vibration and Acoustics 124, 321-324] and overcomes difficulties in satisfying the initial conditions that where noted by Schmidt and Gaul [Schmidt, A., Gaul, L., 2006. On a critique of a numerical scheme for calculation of fractionally damped dynamical systems. Mechanics Research Communications 33, 99-107]. We tested our procedure on several examples. The results show good agreement with the results obtained by other methods. © 2008 Elsevier Ltd. All rights reserved. | URI: | https://open.uns.ac.rs/handle/123456789/11848 | ISSN: | 00936413 | DOI: | 10.1016/j.mechrescom.2008.05.003 |
Appears in Collections: | FTN Publikacije/Publications |
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