P. MOKHTARY . DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia, Series B, 2016 , 36(2) : 560 -578 . DOI: 10.1016/S0252-9602(16)30021-2

[1] Atkinson K E. The Numerical Solution of Integral Equations of the Second Kind. Cambridge, 1997
[2] Awawdeh F, Rawashdeh E A, Jaradat H M. Analytic solution of fractional integro-differential equations. Ann Univ Craiova Math Comput Sci Ser, 2011, 38:1-10
[3] Bagley R L, Torvik P J. A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol, 1983, 27:201-210
[4] Brunner H. Collocation Methods for Volterra and Related Functional Equations. Cambridge:Cambridge University Press, 2004
[5] Caputo M. Linear models of dissipation whose Q is almost frequency independent II. Geophys J Roy Astron Soc, 1967, 13:529-539
[6] Canuto C, Hussaini M Y, Quarteroni A, Zang T A. Spectral Methods, Fundamentals in Single Domains. Berlin:Springer-Verlag, 2006
[7] Chen Y, Tang T. Convergence analysis of the Jacobi spectral collocation methods for volterra integral equations with a weakly singular kernel. Math Comput, 2010, 79:147-167
[8] Diethelm K. The Analysis of Fractional Differential Equations. Berlin:Springer-Verlag, 2010
[9] Doha E H, Bhrawy A H, Ezz-Eldien S S. A new Jacobi operational matrix:an application for solving fractional differential equations. Appl Math Model, 2012, 36:4931-4943
[10] El-Borai Mahmoud M, Debbouche Amar. On some fractional integro-differential equations with analytic semigroups. Int J Contemp Math Sciences, 2009, 4(28):1361-1371
[11] Eslahchi M R, Dehghan M, Parvizi M. Application of the collocation method for solving nonlinear fractional integro-differential equations. J Comput Appl Math, 2014, 257:105-128
[12] Ghoreishi F, Mokhtary P. Spectral collocation method for multi-order fractional differential equations. Int J Comput Math, 2014, 11(5):23
[13] Guo Ben-Yu, Shen Jie, Wang Li-Lian. Optimal spectral-galerkin methods using generalized Jacobi polyno-mials. J Sci Comput, 2006, 27:305-322
[14] Guo Ben-Yu, Shen Jie, Wang Li-Lian. Generalized Jacobi polynomials/functions and their applications. Appl Numer Math, 2009, 59:1011-1028
[15] Huang L, Li X F, Zhao Y L, Duan X Y. Approximate solution of fractional integro-differential eqations by Taylor expansion method. Comput Math Appl, 2011, 62:1127-1134
[16] Hesthaven J S, Gottlieb S, Gottlieb D. Spectral Methods for Time-Dependent Problems. Cambridge Uni-versity Press, 2007
[17] Kantrovich L V. Functional analysis and applied mathematics. Usp Mat Nauk, 1984, 3:89-185
[18] Kantrovich L V, Akilov G P. Functional Analysis in Normed Spaces (Funktsional'nyi analiz v normirovan-nykh prostranstvakh). Moscow:Fizmatgiz, 1959
[19] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations. Amesterdam:Elsevier, 2006
[20] Khader M M, Sweilam N H. On the approximate solutions for system of fractional integro-differential equations using chebyshev pseudo-spectral method. Appl Math Model, 2013, 27(24):819-9828
[21] Mittal R C, Nigam R. Solution of fractional calculus and fractional integro-differential equations by adomian decomposition method. Int J Appli Math Mech, 2008, 4(4):87-94
[22] Ma Xiaohua, Huang C. Numerical solution of fractional integro-differential equations by Hybrid collocation method. Appl Math Comput, 2013, 219:6750-6760
[23] Ma Xiaohua, Huang C. Spectral collocation method for linear fractional integro-differential equations. Appl Math Model, 2014, 38(4):1434-1448
[24] Mokhtary P, Ghoreishi F. The L²-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations. Numer Algorithms, 2011, 58:475-496
[25] Mokhtary P, Ghoreishi F. Convergence analysis of spectral Tau method for fractional Riccati differential equations. Bull Iranian Math Soc, 2014, 40(5):1275-1290
[26] Mokhtary P. Operational Tau method for non-linear FDEs. Iranian Journal of Numerical Analysis and Optimization, 2014, 4(2):43-55
[27] Mokhtary P. Reconstruction of exponentially rate of convergence to Legendre-collocation solution of a class of fractional integro-differential equations. J Comput Appl Math, 2014, 279:145-158
[28] Nazari D, Shahmorad S. Application of the fractionl differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions. J Comput Appl Math, 2010, 234:883-891
[29] Oldham K B, Spanier J. The Fractional Calculus. New York:Academic Press, 1974
[30] Olmstead W E, Handelsman R A. Diffusion in a semi-infinite region with nonlinear surface dissipation. SIAM Rev, 1976, 18:275-291
[31] Podlubny I. Fractional Differential Equations. Academic Press, 1999
[32] Porter D, Stirling David S G. Integral Equations, A Practical Treatment, from Spectral Theory to Appli-cations. New York:Cambridge University Press, 1990
[33] Rawashdeh E A. Numerical solution of fractional integro-differential equations by collocation method. Appl Math Comput, 2006, 176:1-6
[34] Shen Jie, Tang Tao, Wang Li-Lian. Spectral Methods, Algorithms, Analysis and Applications. Springer, 2011
[35] Xianjuan Li, Tang T. Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind. Front Math China, 2012, 7(1):69-84
[36] Zhu Li, Fan Qibin. Numerical solution of nonlinear fractional order Volterra integro differential equations by SCW. Commun Nonlinear Sci Numer Simul, 2013, 18(15):1203-1213
[37] Vainikko G M. Galerkin's perturbation method and the general theory of approximate methods for non-linear equations. USSR Computational Mathematics and Mathematical Physics, 1967, 7(4):1-41
[38] Yang Yin. Jacobi spectral galerkin methods for fractional integro-differential equations. Calcolo. DOI:10.1007/s10092-014-0128-6.
[39] Yang Yin, Chen Yanping, Huang Yanqing. Convergence analysis of the Jacobi spectral-collocation method for fractional integro-differential equations. Acta Mathematica Scientia, 2014, 34B(3):673-690