Numerical solution of nonlinear fractional differential equations by spline collocation methods

Diethelm, 2010, vol. 2004 Brunner, 2001, Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels, SIAM J. Numer. Anal., 39, 957, 10.1137/S0036142900376560 Kilbas, 2006, vol. 204 Podlubny, 1999 Samko, 1993 Diethelm, 2004, Detailed error analysis for a fractional Adams method, Numer. Algorithms, 36, 31, 10.1023/B:NUMA.0000027736.85078.be Diethelm, 2006, Pitfalls in fast numerical solvers for fractional differential equations, J. Comput. Appl. Math., 229, 382 Ford, 2009, Systems-based decomposition schemes for approximate solution of multi-term fractional differential equations, J. Comput. Appl. Math., 186, 482 Lepik, 2009, Solving fractional integral equations by Haar wavelet method, Appl. Math. Comput., 214, 468 Hamarsheh, 2010, A numerical method for solution of semidifferential equations, Mat. Vesnik, 62, 117 Doha, 2011, A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order, Comput. Math. Appl., 62, 2364, 10.1016/j.camwa.2011.07.024 Pedas, 2011, On the convergence of spline collocation methods for solving fractional differential equations, J. Comput. Appl. Math., 235, 3502, 10.1016/j.cam.2010.10.054 Pedas, 2011, Spline collocation methods for linear multi-term fractional differential equations, J. Comput. Appl. Math., 236, 167, 10.1016/j.cam.2011.06.015 Pedas, 2012, Piecewise polynomial collocation for linear boundary value problems of fractional differential equations, J. Comput. Appl. Math., 236, 3349, 10.1016/j.cam.2012.03.002 Vainikko, 1993, vol. 1549 Brunner, 2004, vol. 15 Brunner, 1999, The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations, Math. Comp., 1079, 10.1090/S0025-5718-99-01073-X Diethelm, 2002, Analysis of fractional differential equations, J. Math. Anal. Appl., 265, 229, 10.1006/jmaa.2000.7194 Diethelm, 2004, Multi-order fractional differential equations and their numerical solution, Appl. Math. Comput., 154, 621 Lakshmikantham, 2008, General uniqueness and monotone iterative technique for fractional differential equations, Appl. Math. Lett., 21, 828, 10.1016/j.aml.2007.09.006 Vasundhara Devi, 2009, Nonsmooth analysis and fractional differential equations, Nonlinear Anal., 70, 4151, 10.1016/j.na.2008.09.003 Zhou, 2009, Existence and uniqueness of solutions for a system of fractional differential equations, Fract. Calc. Appl. Anal., 12, 195 Dutkiewicz, 2010, On the Aronszajn property for an implicit differential equation of fractional order, Z. Anal. Anwend., 29, 429, 10.4171/ZAA/1416 Baˇleanu, 2010, On the global existence of solutions to a class of fractional differential equations, Comput. Math. Appl., 59, 1835, 10.1016/j.camwa.2009.08.028 Li, 2012, Existence and uniqueness of solutions for initial value problem of nonlinear fractional differential equations, Abstr. Appl. Anal., 14 Pedas, 1994, The smoothness of solutions to nonlinear weakly singular integral equations, Z. Anal. Anwend., 13, 463, 10.4171/ZAA/501 Pedas, 2006, Integral equations with diagonal and boundary singularities of the kernel, Z. Anal. Anwend., 25, 457 Johnson, 2002, The curious history of Faà di Bruno’s formula, Amer. Math. Monthly, 109, 217 G. Vainikko, Analysis of Discretization Methods, Tartu University, Tartu, 1976 (in Russian). Vainikko, 1976 Vainikko, 1978, Approximative methods for nonlinear equations (two approaches to the convergence problem), Nonlinear Anal., 2, 647, 10.1016/0362-546X(78)90013-5