References
[1]. R. P. Agarwal, B. de Andrade, and C. Cuevas, (2010). Weighted pseudo-almost periodic solutions of a class of
semilinear fractional differential equations, Nonlinear Analysis: Real World Applications, 11 (5), 3532--3554.
[2]. R. P. Agarwal, V. Lakshmikantham, and J. J. Nieto, (2010). On the concept of solution for fractional differential equations
with uncertainty, Nonlinear Analysis: Theory,Methods & Applications, 72(6), 2859--2862.
[3]. R. Garrappa and M. Popolizio, (2011). On the use of matrix functions for fractional partial differential equations,
Mathematics and Computers in Simulation, 81 (5), 1045--1056.
[4]. R. Hilfer, (2000). Applications of Fractional Calculus in Physics, World Scientific Publishing, River Edge, NJ, USA.
[5]. Y. Khan, N. Faraz, A. Yildirim, and Q. Wu, (2011). Fractional variational iteration method for fractional initial-boundary
value problems arising in the application of nonlinear science, Computers & Mathematics with Applications, 62 (5), 2273--
2278.
[6]. Z. Odibat, (2011). On Legendre polynomial approximation with the VIM or HAM for numerical treatment of nonlinear
fractional differential equations, Journal of Computational and Applied Mathematics, 235 (9), 2956--2968.
[7]. I. Podlubny, (1999). Fractional Differential Equations of Mathematics in Science and Engineering, Academic Pres, San
Diego, Calif, USA, (198).
[8]. S. G. Samko, A. A. Kilbas, and O. I. Marichev, (1993). Fractional Integrals and Derivatives: Theory and Applications,
Gordon and Breach, Yverdon, Switzerland.
[9]. K. Diethelm, N. J. Ford, (2001). Analysis of fractional differential equations, Numerical Analysis Report, 377, 1360-1725.
[10]. S. Das, (2008). Functional Fractional Calculus for System Identification and Controls, Springer, New York.
[11]. K. Diethelm, (1997). An algorithm for the numerical solution of differential equations of fractional order, Electron. Trans.
Numer. Anal., (5), 1-6.
[12]. M. Enelund, B.L. Josefson, (1997). Time-domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations, AIAA J., 35 (10), 1630-1637.
[13]. I. Hashim, O. Abdulaziz, S. Momani, (2009). Homotopy analysis method for fractional IVPs, Commun. Nonlinear Sci.
Numer. Simul., 14, 674-684.
[14]. J.H. He, (1998). Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer
Methods in Applied Mechanics and Engineering, 167 (1-2), 57-68.
[15]. M.M. Meerschaert, C. Tadjeran, (2004). Finite difference approximations for fractional advection-dispersion flow
equations, J. Comput. Appl. Math., 172 (1), 65-77.
[16]. J.H. He, (1999). Variational iteration method -- A kind of non-linear analytical technique: Some examples, International
Journal of Non-Linear Mechanics, 34, 699-708.
[17]. M. Inc, (2008). The approximate and exact solutions of the space- and time- fractional Burger's equations with initial
conditions by variational iteration method, J. Math. Anal. Appl., 345, 476-484.
[18]. J.H. He, (1999). Homotopy perturbation technique, Comput. Methods Appl. Mech. Engng., 178 (3-4), 257-262.
[19]. N.H. Sweilam, M.M. Khader, R.F. Al-Bar, (2008). Homotopy perturbation method for linear and nonlinear system of
fractional integro-differential equations, Int. J. of Computational Mathematics and Numerical Simulation, 1 (1), 73-87.
[20]. H. Jafari, V. Daftardar-Gejji, (2006). Solving linear and nonlinear fractional diffusion and wave equations by Adomian
decomposition, Appl. Math. and Comput., 180, 488-497.
[21]. M.M. Khader, (2011). On the numerical solutions for the fractional diffusion equation, Communications in Nonlinear
Science and Numerical Simulation, 16, 2535-2542.
[22]. E.A. Rawashdeh, (2006). Numerical solution of fractional integro-differential equations by collocation method, Appl.
Math. Comput., 176, 1-6.
[23]. W.W. Bell, (1968). Special Functions For Scientists and Engineers, Great Britain, Butler and Tanner Ltd, Frome and London.
[24]. M.M. Khader, A.S. Hendy, (2012). The approximate and exact solutions of the fractional-order delay differential
equations using legendre seudospectral method, International Journal of Pure and Applied Mathematics, 74 (3), 287-297.