Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results

Journal

2013 | 11 | 10 | 1372-1376

Article title

Numerical solution of fractional differential equations by using fractional B-spline

Content

Title variants

Languages of publication

EN

Abstracts

EN
In this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.

Publisher

Journal

Year

Volume

11

Issue

10

Pages

1372-1376

Physical description

Dates

published
1 - 10 - 2013
online
19 - 12 - 2013

Contributors

  • International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, P. Bag X2046, Mmabatho, 2735, South Africa
  • Department of Mathematics, Imam Khomeini International, Qazvin, Iran
  • Department of Mathematics, University of Mazandaran, 47416-95447, Babolsar, Iran

References

  • [1] M. Caputo, J. Roy. Austral. Soc. 13, 529 (1967) http://dx.doi.org/10.1111/j.1365-246X.1967.tb02303.x[Crossref]
  • [2] J. G. Lu, G. Chen, Chaos Soliton. Fract. 27, 685 (2006) http://dx.doi.org/10.1016/j.chaos.2005.04.037[Crossref]
  • [3] R. L. Bagley, P.J. Torvik, AIAA J. 21, 741 (1983) http://dx.doi.org/10.2514/3.8142[Crossref]
  • [4] L. Gaul, P. Klein, S. Kempfle, Mech. Res. Commun. 16, 297 (1989) http://dx.doi.org/10.1016/0093-6413(89)90067-0[Crossref]
  • [5] D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos (World Scientific, Boston, 2012)
  • [6] K. B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, New York and London, 1974)
  • [7] V. Daftardar-Gejji, H. Jafari, J. Math. Anal. Appl. 189, 541 (2007)
  • [8] S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method (CRC Press, Boca Raton, Chapman & Hall, 2003) http://dx.doi.org/10.1201/9780203491164[Crossref]
  • [9] H. Jafari, S. Das, H. Tajadodi, Journal of King Saud University-Science 23, 151 (2011) http://dx.doi.org/10.1016/j.jksus.2010.06.023[Crossref]
  • [10] H. Jafari, N. Kadkhoda, H. Tajadodi, S.A. Hosseini-Matikolai, Int. J. Nonlin. Sci. Num. 11, 271 (2010)
  • [11] H. Jafari, Sh. Momani, Phys. Lett. A 370, 388 (2007) http://dx.doi.org/10.1016/j.physleta.2007.05.118[Crossref]
  • [12] H. Jafari, H. Tajadodi, D. Baleanu, Fract. Calc. Appl. Anal. 16, 109 (2013).
  • [13] H. Jafari, H. Tajadodi, Int. J. Diff. Eqn. 2010, 764738 (2010)
  • [14] G. C. Wu, E.W.M. Lee, Phys. Lett. A 374, 2506 (2010) http://dx.doi.org/10.1016/j.physleta.2010.04.034[Crossref]
  • [15] G. C. Wu, Therm. Sci. 16, 1257 (2012) http://dx.doi.org/10.2298/TSCI1204257W[Crossref]
  • [16] G. C. Wu, Int. Rev. Chem. Eng. 4, 505 (2012)
  • [17] G. C. Wu, D. Baleanu, Adv. Difference Equ. 2013, 18 (2013) http://dx.doi.org/10.1186/1687-1847-2013-18[Crossref]
  • [18] H. Jafari, S.A. Yousefi, M.A. Firoozjaee, Commun. Frac. Calc. 2, 9 (2011)
  • [19] W. J. Richard, Comput. Fluids 34, 121 (2005) http://dx.doi.org/10.1016/j.compfluid.2004.03.005[Crossref]
  • [20] E. A. Rawashdeh, Appl. Math. Comput. 176, 1 (2006) http://dx.doi.org/10.1016/j.amc.2005.09.059[Crossref]
  • [21] C. K. Chui, Multivariate splines, CBMS Series in Applied Mathematics no 54 (SIAM, Philadelphia, PA, 1988)
  • [22] C. de Boor, K. Höllig, S. Riemenschneider, Box splines, Appl. Math. Sci. 98 (Springer-Verlag, New York, 1993) http://dx.doi.org/10.1007/978-1-4757-2244-4[Crossref]
  • [23] G. Nürnberger, Approximation by Spline Functions (Springer-Verlag, Berlin, 1989) http://dx.doi.org/10.1007/978-3-642-61342-5[Crossref]
  • [24] W. Schempp, Contemporary Mathematics 7, Amer. Math. Soc. (1982)
  • [25] T. Blu, M. Unser, IEEE T. Signal Proces. 47, 2796 (1999) http://dx.doi.org/10.1109/78.790660[Crossref]
  • [26] B. Forster, T. Blu, M. Unser, Appl. Comput. Harmon. Anal. 20, 261 (2006) http://dx.doi.org/10.1016/j.acha.2005.07.003[Crossref]
  • [27] I. Podlubny, Fractional Differential Equations (Academic Press, SanDiego, 1999)
  • [28] K. E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind (Cambridge University Press, Atkinson Kendall, United States of America, 1997) http://dx.doi.org/10.1017/CBO9780511626340[Crossref]
  • [29] Yu. Luchko, R. Gorenflo, Acta Math. Vietnamica 24, 207 (1999)
  • [30] M. Unser, T. Blu, SIAM Rev. 42, 43 (2000) http://dx.doi.org/10.1137/S0036144598349435[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-013-0222-4
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.