A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

[1] A.H. Bhrawy, A.S. Alo, The operational matrix of fractional integration for shifted
Chebyshev polynomials, Applied Mathematics Letters, 26 (2013) 25-31.
[2] E. H. Doha, A.H. Bhrawy, S. S. Ezz-Eldien , A Chebyshev spectral method based on
operational matrix for initial and boundary value problems of fractional order, Comput.
Math. Appl., 62 (2011) 2364-2373.
[3] A. Nkwanta and E.R. Barnes, Two Catalan-type Riordan arrays and their connections to
the Chebyshev polynomials of the rst kind, Journal of Integer Sequences, 15 (2012) 1-19.
[4] Fox, Lslie and Ian Bax Parker, Chebyshev Polynomials in Numerical Analysis, Oxford
university press, London, vol. 29, 1968
[5] K. Diethelm, The analysis of fractional dierential equations, Berlin: Springer-Verlag,
2010.
[6] K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
[7] K.S. Miller, B. Ross, An Introduction to The Fractional Calculus and Fractional Dierential
Equations, Wiley, New York, 1993.
[8] I. Podlubny, Fractional Dierential Equations, Academic Press, San Diego, 1999.
[9] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential
Equations, Elsevier, San Diego, 2006.
[10] X. Li, Numerical solution of fractional dierential equations using cubic B-spline wavelet
collocation method, Commun Nonlinear Sci Numer Simulat., 17 (2012) 3934-3946.
[11] A. Saadatmandi, M. Dehghan, M. R. Azizi, The Sinc-Legendre collocation method for
a class of fractional convection-diusion equations with variable coecients, Commun
Nonlinear Sci Numer Simulat., 17 (2012) 4125-4136.
[12] M. Lakestani, M. Dehghan, S. Irandoust-pakchin, The construction of operational matrix
of fractional derivatives using B-spline functions, Commun Nonlinear Sci Numer Simulat,
17 (2012) 1149-1162.
[13] A. Saadatmandi, M. Dehghan, A new operational matrix for solving fractional-order
dierential equations, Comput. Math. Appl., 59 (2010) 1326-1336.
[14] S. Kazem, S. Abbasbandy, S. Kumar, Fractional-order Legendre functions for solving
fractional-order dierential equations, Applied Mathematical Modelling, In press,
http://dx.doi.org/10.1016/j.apm.2012.10.026
[15] A. Kayedi-Bardeh, M. R. Eslahchi, M. Dehghan, A method for obtaining the operational
matrix of fractional Jacobi functions and applications, Journal of Vibration and Control,
In press, DOI: 10.1177/1077546312467049.
[16] C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods. Fundamentals
in Single Domains, Springer-Verlag, Berlin, 2006.
[17] Z .M. Odibat, N. T. Shawagfeh, Generalized Taylor's formula, Applied Mathematics
and Computation 186(2007) 286-293.

[18] S. Esmaeili, M. Shamsi, Y. Luchko, Numerical solution of fractional dierential equations
with a collocation method based on Muntz polynomials, Comput. Math. Appl., 62
(2011) 918-929.