Legendre multiwavelet collocation method for solving the linear fractional time delay systems

• Authors: Sohrab Yousefi , Ali Lotfi
• Languages of publication: EN

Abstracts

EN

In this article the Legendre multiwavelet basis with aid of collocation method has been applied to give approximate solution for fractional delay systems. The properties of Legendre multiwavelet are presented. These properties together with the collocation method are then utilized to reduce the problem to the solution of algebraic system. Numerical results and comparison with exact solutions in the cases when we have exact solution are given in test examples in order to demonstrate the applicability and efficiency of the method.

Keywords

EN

Legendre multiwavelet; time delay system; collocation method; Caputo fractional derivative; Riemann-Liouville fractional integral

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1463-1469

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Sohrab Yousefi

• Department of Mathematics, Shahid Beheshti University, G.C. Tehran, Iran

author

Ali Lotfi

• Department of Mathematics, Shahid Beheshti University, G.C. Tehran, Iran

References

• [1] R.L. Bagley, P.J. Torvik, J. Rheol. 27, 201 (1983) http://dx.doi.org/10.1122/1.549724[Crossref]
• [2] R.L. Bagley, P.J. Torvik, AIAA J. 23, 918 (1985) http://dx.doi.org/10.2514/3.9007[Crossref]
• [3] R. L. Magin, Crit. Rev. Biomed. Eng. 32, 1 (2004) http://dx.doi.org/10.1615/CritRevBiomedEng.v32.10[Crossref]
• [4] T. S. Chow, Phys. Lett. A. 342, 148 (2005) http://dx.doi.org/10.1016/j.physleta.2005.05.045[Crossref]
• [5] M. Zamani, M. Karimi-Ghartemani, N. Sadati, Journal of Fractional Calculus and Applied Analysis (FCAA) 10, 169 (2007)
• [6] J.A. Machado, Syst. Anal. Model. Sim. 27, 107 (1997)
• [7] I.S. Jesus, J.A. Machado, Nonlinear Dynam. 54, 263 (2008) http://dx.doi.org/10.1007/s11071-007-9322-2[Crossref]
• [8] I. Podlubny, IEEE T. Automat. Contr. 44, 208 (1999) http://dx.doi.org/10.1109/9.739144[Crossref]
• [9] X. Zhang, Appl. Math. Comput. 197, 407 (2008) http://dx.doi.org/10.1016/j.amc.2007.07.069[Crossref]
• [10] W. deng, C. Li, J. Lu, Nonlinear Dynam. 48, 409 (2007) http://dx.doi.org/10.1007/s11071-006-9094-0[Crossref]
• [11] M. P. Lazarevic, A. M. Spasic, Math. Comput. Model. 49, 475 (2009) http://dx.doi.org/10.1016/j.mcm.2008.09.011[Crossref]
• [12] C.K. Chui, Wavelets: A mathematical tool for signal analysis (SIAM, Philadelphia PA, 1997) http://dx.doi.org/10.1137/1.9780898719727[Crossref]
• [13] Q. Ming, C. Hwang, Y.P. Shih, Int. J. Numer. Meth. Eng. 39, 2921 (1996) http://dx.doi.org/10.1002/(SICI)1097-0207(19960915)39:17<2921::AID-NME983>3.0.CO;2-D[Crossref]
• [14] G. Beylkin, R. Coifman, V. Rokhlinn, Commun. Pur. Appl. Math. 44, 141 (1991) http://dx.doi.org/10.1002/cpa.3160440202[Crossref]
• [15] S. A. Yousefi, A. Lotfi, M. Dehghan, J. Vib. Control 17, 2059 (2011) http://dx.doi.org/10.1177/1077546311399950[Crossref]
• [16] A. Saadatmandi, M. Dehghan, J. Vib. Control 17, 2050 (2011) http://dx.doi.org/10.1177/1077546310395977[Crossref]
• [17] S. A. Yousefi, Numer. Meth. Part. D. E. 26, 535 (2010)
• [18] C. Canuto, M. Y. Hussaini, A. Quarternioni, T. A. Zang, Spectral methods in fluid dynamics (Springer-Verlag, Berlin, 1988) http://dx.doi.org/10.1007/978-3-642-84108-8[Crossref]

Identifiers

DOI

10.2478/s11534-013-0283-4