Document Type: Research Paper

**Authors**

Department of Mathematics, Faculty of Mathematics, Yazd University, Yazd, Islamic Republic of Iran

**Abstract**

In this paper, we develop an efficient Legendre wavelets collocation method for well known time-fractional heat equation. In the proposed method, we apply operational matrix of fractional integration to obtain numerical solution of the inhomogeneous time-fractional heat equation with lateral heat loss and Dirichlet boundary conditions. The power of this manageable method is confirmed. Moreover, the use of Legendre wavelets is found to be accurate, simple and fast.

**Keywords**

Wien, New York, 1997.

[2] K. S. Miller and B. Ross,

Wiley, New York, 1993.

[3] K. B. Oldham and J. Spanier,

[4] I. Podlubny,

[5] I. Podlubny.

Sciences, Institute of Experimental Physics, Kosice, Slovakia, November 1994, 18p.

[6] R. Gorenflo and F. Mainardi,

(1997), 223–276.

[7] W. R. Schneider and W. Wyess,

[8] U. Lepik,

1879.

[9] U. Anderson and B. Engquist,

Model, 7(1999), 151–164.

[10] C. Cattani,

1(2004), 45–63.

[11] N. Coult,

Anal, 21(2001), 360–375.

[12] X. Chen, J. Xiang, B. Li, and Z. He,

[13] G. Hariharan, K. Kannan, and K.R. Sharma,

Comput, 211(2)(2009), 284–292.

[14] P. Mrazek and J. Weickert,

Commun. Image. Represent, 18(2007),162–175.

[15] W. Fan and P. Qiao,

[16] J. E. Kim, G.-W. Yang, and Y.Y. Kim,

Math., 40(2003), 6473–6496.

[17] Y. Shen and W. Li,

Math. Comput., 150 (2)(2004),417–438.

[18] Z. Chun and Z. Zheng,

[19] H. F. Lam and C. T. Ng,

[20] J. Majak, M. Pohlak, M. Eerme, and T. Lepikult, Weak formulation based haar wavelet method for solving

differential equations, Appl. Math. Comput., 211(2009), 488–494.

[21] L. M. S. Castro, A. J. M. Ferreira, S. Bertoluzza, R.C. Patra, and J.N. Reddy,

[22] M. H. Heydari, M. R. Hooshmandasl, M. F. Maalek Ghaini and F. Fereidouni,

Elem., 37(2013),1331-1338.

[23] L. Nanshan and E. B. Lin,

Numer. Methods Partial Dierential Equations, 26(1):81–94, 2009.

[24] M. U. Rehman and R. A. Khan,

Commun. Nonlinear Sci. Numer. Simul., 227(2)(2009), 234–244.

[25] A. Kilicman and Z.A. Al Zhour,

Appl. Math. Comput., 187(1)(2007), 250–65.

[26] M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini and F. Mohammadi,

2012. doi:10.1155/2012/542401.

[27] A. M. Wazwaz,

Volume 1, Issue 1

Summer and Autumn 2014

Pages 19-31