E. Babolian and M. Mordad, Numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions, Comput. Math. Appl. 62 (2011), no. 1, 187--198.
S. Beheshti, H. Khosravian-Arab and I. Zare, Numerical solution of fractional differential equations by using the Jacobi polynomials, J. Basic. Appl. Sci. Res. 2 (2012), no. 5, 4894--4902.
A.H. Bhrawy, M.M. Tharwat and A. Yildirim, A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations, Appl. Math. Model. 37 (2013), no. 6, 4245--4252.
T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
S. Das, Functional Fractional Calculus For System Identification and Controls, Springer, New York, 2008.
M. Dehghan and A. Saadatmandi, A Tau method for the one-dimensional parabolic inverse problem subject to temperature overspecification, Comput. Math. App 52 (2006), no. 6-7, 933--940.
K. Diethelm and N.J. Ford, Numerical solution of the Bagley-Torvik equation, BIT 42 (2002), no. 3, 490--507.
K. Diethelm, N.J. Ford and A.D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equation, Nonlinear Dynam. 29 (2002), no. 1, 3--22.
E.H. Doha, A.H. Bhrawy and R.M. Hafez, On shifted Jacobi spectral method for high order multi-point boundary value problems, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), no. 10, 3802--3810.
E.H. Doha and A.H. Bhrawy, S. S. Ezz-Eldien, A new Jacobi operational matrix :an application for solving fractional differential equations, Appl. Math. Model. 36 (2012), no. 10, 4931--4943.
A. El-Mesiry, A. El-Sayed and H. El-Saka, Numerical methods for multi-term fractional (arbitrary) orders differential equations, Appl. Math. Comput. 160 (2005), no. 3, 683--699.
V.J. Ervin and J.P. Roop, Variational formulation for the stationary fractional advection dispersion equation, Numer. Methods Partial Differential Equations 22 (2006), no. 3, 558--576.
M.R. Eslahchi and M. Dehghan,Application of Taylor series in obtaining the orthogonal operational matrix, Comput. Math. Appl. 61 (2011), no. 9, 2596--2604.
I. Grigorenko and E. Grigorenko, Chaotic dynamics of the fractional Lorenz system, Phys. Rev. Lett. 91 (2003), no. 3, 034101--034104.
D.N. Hào and H.J. Reinhardt, A. Schneider, Stable approximation of fractional derivatives of rough functions, BIT 35 (1995), no. 4, 488--503.
I. Hashim, O. Abdulaziz and S. Momani, Homotopy analysis method for fractional IVPs, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), no. 3, 674--684.
J.H. He Nonlinear oscillation with fractional derivative and its applications, in: Proceedings of the International Conference on Vibrating Engineering, Dalian, Chaina, 1998.
J.H. He, Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol. 15 (1999), no. 2, 86--90.
J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods. Appl. Mech. Engrg. 167 (1998), no. 1-2, 57--68.
H. Jafari, S. Das and H. Tajadodi, Solving a multi-order fractional differential equation using homotopy analysis method, J. King Saud Univ. Sci. 23 (2011), no. 2, 151--155.
S. Kazem, An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations, Appl. Math. Model. 37 (2013), no. 3, 1126--1136.
A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, San Diego, 2006.
E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 1978.
P. Kumar and O.P. Agrawal, An approximate method for numerical solution of fractional differential equations, Signal Process. 86 (2006), no. 10, 2602--2610.
Y. Li, Solving a nonlinear fractional differential equation using Chebyshev wavelets, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 9, 2284--2292.
Y. Li and N. Sun, Numerical solution of fractional differential equations using the generalized block pulse operational matrix, Comput. Math. Appl. 62 (2011), no. 3, 1046--1054.
Y. Li and W. Zhao, Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations, Appl. Math. Comput. 216 (2010), no. 8, 2276--2285.
F. Liu, V. Anh and I. Turner, Numerical solution of the space fractional Fokker-Planck equation, J. Comput. Appl. Math. 166 (2004), no. 1, 209--219.
Y. Luchko and R. Gorenflo, The initial value problem for some fractional differential equations with the Caputo derivatives,Fachbereich Mathematik und Informatik, Berlin 1998.
Q.M. Mdallal, M.I. Syam and M.N. Anwar, A collocation-shooting method for solving fractional boundary value problems, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 12, 3814--3822.
K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.
Z. Odibat, S. Momani and H. Xu, A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations, Appl. Math. Model. 34 (2010), no. 3, 593--600.
K.B. Oldham and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Dover Publications, New York, 2006.
I. Podlubny, Fractional Differential Equations, Academic Press , San Diego, 1999.
E.A. Rawashdeh, Numerical solution of fractional integro-differential equations by collocation method, Appl. Math. Comput. 176 (2006), no. 1, 1--6.
S.S. Ray and R.K. Bera, Solution of an extraordinary differential equation by adomian decomposition method, J. Appl. Math. 2004 (2004), no. 4, 331--338.
T.J. Rivlin, An Introduction to the Approximation of Functions, Dover Publications, New York, 2003.
A. Saadatmandi and M. Dehghan, A new operational matrix for solving fractional order differential equations, Comput. Math. Appl. 59 (2010), no. 3, 1326--1336.
J. Shen and T. Tang, High Order Numerical Methods and Algorithms, Chinese Science Press, Beijing, 2005.
N.H. Sweilam, M.M. Khader and R.F. Al-Bar, Numerical studies for a multi-order fractional differential equation, 371 (2007), no. 1, 26--33.
G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. Providence, RI, 1975.
M.P. Tripathi, K. Vipul, R.K.P. Baranwal and O.P. Singh, A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions, Commun. Nonlinear. Sci. Numer. Simul. 18 (2013), no. 6, 1327--1340.
S. Yang, A. Xiao and H. Su, Convergence of the variational iteration method for solving multi-order fractional differential equations, Comput. Math. Appl. 60 (2010), no. 10, 2871--2879.
S.B. Yuste, Weighted average finite difference methods for fractional diffusion equations, J. Comput. Phys. 216 (2006), no. 1, 264--274.