Wavelet collocation method for solving multiorder fractional differential equations

Journal of Applied Mathematics

Volumn 2012, Issue , 2012, Pages

  Heydari, M H ^a   Hooshmandasl, M R ^a   Maalek Ghaini, F M ^a   Mohammadi, F ^a  

^a YAZD UNIVERSITY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84858110986     PISSN: 1110757X     EISSN: 16870042     Source Type: Journal    
DOI: 10.1155/2012/542401     Document Type: Article

References (28)

1. Carpinteri A., Mainardi F., Fractals and Fractional Calculus in Continuum Mechanics 1997 New York, NY, USA Springer
2. Miller K. S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 New York, NY, USA John Wiley Sons xvi+366
3. Oldham K. B., Spanier J., The Fractional Calculus 1974 New York, NY, USA Academic Press xiii+234
4. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340
5. Podlubny I., Fractional-order systems and fractional-order controllers Report 1994 UEF-03-94 Kosice, Slovakia Slovak Academy of Sciences, Institute of Experimental Physics
6. Gorenflo R., Mainardi F., Fractional calculus: integral and differential equations of fractional order Fractals and Fractional Calculus in Continuum Mechanics 1997 378 Vienna, Austria Springer 223 276
7. Schneider W. R., Wyss W., Fractional diffusion and wave equations Journal of Mathematical Physics 1989 30 1 134 144
8. Li Y., Solving a nonlinear fractional differential equation using Chebyshev wavelets Communications in Nonlinear Science and Numerical Simulation 2010 15 9 2284 2292
9. Diethelm K., Ford N. J., Multi-order fractional differential equations and their numerical solution Applied Mathematics and Computation 2004 154 3 621 640
10. Diethelm K., Luchko Y., Numerical solution of linear multi-term initial value problems of fractional order Journal of Computational Analysis and Applications 2004 6 3 243 263 (Pubitemid 44387224)
11. Diethelm K., Multi-term fractional differential equations multi-order fractional differential systems and their numerical solution Journal Européen des Systmes Automatisés 2008 42 665 676
12. El-Sayed A. M. A., El-Mesiry A. E. M., El-Saka H. A. A., Numerical solution for multi-term fractional (arbitrary) orders differential equations Computational Applied Mathematics 2004 23 1 33 54
13. El-Sayed A. M. A., El-Mesiry A. E. M., El-Saka H. A. A., Numerical methods for multi-term fractional (arbitrary) orders differential equations Applied Mathematics and Computation 2005 160 3 683 699
14. El-Sayed A. M. A., El-Kalla I. L., Ziada E. A. A., Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations Applied Numerical Mathematics 2010 60 8 788 797
15. Daftardar-Gejji V., Jafari H., Solving a multi-order fractional differential equation using Adomian decomposition Applied Mathematics and Computation 2007 189 1 541 548 (Pubitemid 46734260)
16. Edwards J. T., Ford N. J., Simpson A. C., The numerical solution of linear multiterm fractional differential equations: systems of equations Manchester Center for Numerical Computational Mathematics 2002
17. Diethelm K., Ford N. J., Numerical solution of the Bagley-Torvik equation BIT. Numerical Mathematics 2002 42 3 490 507
18. Wu J. L., A wavelet operational method for solving fractional partial differential equations numerically Applied Mathematics and Computation 2009 214 1 31 40
19. Lepik., Solving fractional integral equations by the Haar wavelet method Applied Mathematics and Computation 2009 214 2 468 478
20. Li Y., Zhao W., Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations Applied Mathematics and Computation 2010 216 8 2276 2285
21. Rehman M. U., Khan R. A., The legendre wavelet method for solving fractional differential equations Communication in Nonlinear Science and Numerical Simulation 2009 227 2 234 244
22. Bujurke N. M., Shiralashetti S. C., Salimath C. S., An application of single-term Haar wavelet series in the solution of nonlinear oscillator equations Journal of Computational and Applied Mathematics 2009 227 2 234 244
23. Babolian E., Masouri Z., Hatamzadeh-Varmazyar S., Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions Computers Mathematics with Applications 2009 58 2 239 247
24. Tavassoli Kajani M., Hadi Vencheh A., Ghasemi M., The Chebyshev wavelets operational matrix of integration and product operation matrix International Journal of Computer Mathematics 2009 86 7 1118 1125
25. Reihani M. H., Abadi Z., Rationalized Haar functions method for solving Fredholm and Volterra integral equations Journal of Computational and Applied Mathematics 2007 200 1 12 20 (Pubitemid 44738292)
26. Khellat F., Yousefi S. A., The linear Legendre mother wavelets operational matrix of integration and its application Journal of the Franklin Institute 2006 343 2 181 190 (Pubitemid 43190065)
27. Razzaghi M., Yousefi S., The Legendre wavelets operational matrix of integration International Journal of Systems Science 2001 32 4 495 502
28. Kilicman A., Al Zhour Z. A., Kronecker operational matrices for fractional calculus and some applications Applied Mathematics and Computation 2007 187 1 250 265 (Pubitemid 46635724)