A Numerical solution for the new model of time-fractional bond pricing‎: ‎Using a multiquadric approximation method

[1] I. Podlubny, Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, 198. Academic Press, Inc., San Diego, CA, 1999.
[2] V. R. Hosseini, W. Chen, and Z. Avazzadeh, Numerical solution of fractional telegraph equation by using radial basis functions, Eng. Anal. Bound. Elem, 38 (2014) 31{39.
[3] Y. Lin and C. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys, 225(2) (2007) 1533{1552.
[4] C. Li, Z. Zhao and, Y. Q. Chen, Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion, Comput. Math. Appl, 62(3) (2011) 855{875.
[5] X. Li and C. Xu, A space-time spectral method for the time fractional diffusion equation, SIAM J. Numer. Anal, 47(3) (2009) 2108{2131.
[6] F. Liu, P. Zhuang, V. Anh, and I. Turner, A fractional-order implicit difference approximation for the space{time fractional diffusion equation, ANZIAM J, 47 (C) (2005) C48{C68.

[7] W. Wyss, The fractional Black-Scholes equation, Fract. Calc. Appl. Anal, 3(1) (2000) 51{62.
[8] G. Jumarie, Derivation and solutions of some fractional Black{Scholes equations in coarsegrained space and time, Application to Merton's optimal portfolio. Comput. Math. Appl, 59(3)
(2010) 1142{1164.
[9] B. Osu and A. Chukwunezu, On the solution to a fractional Black{Scholes equation for the price of an option, Int. J. Math. Anal. Appl, 1(3) (2014) 38{42.
[10] M. A. M. Ghandehari and M. Ranjbar, European option pricing of fractional Black{Scholes model with new Lagrange multipliers, Comput. Methods Differ. Equ, 2(1) (2014) 1{10.
[11] L. Song and W. Wang, Solution of the fractional Black{Scholes option pricing model by nite difference method. Abstr. Appl. Anal, Hindawi Publishing Corporation, (2013).
[12] A. A. Elbeleze, A. Klcman, and B. M. Taib, Homotopy perturbation method for fractional Black{Scholes European option pricing equations using Sumudu transform, Math. Probl. Eng,
2013.
[13] S. Kumar, A. Yildirim, Y. Khan, H. Jafari, K. Sayevand, and L. Wei, Analytical solution of fractional Black-Scholes European option pricing equation by using Laplace transform, J.Fractional Calc. Appl, 2(8) (2012) 1{9.
[14] P. Wilmott, S. Howison and J. Dewynne, The mathematics of  nancial derivatives: A student introduction, Cambridge University Press, 1995.
[15] Y. Yajima, On Estimation of Long-Memory time series models, Austral. J. Statist, 27(3) (1985) 303{320.
[16] B. B. Mandelbrot, When can price be arbitraged efficiently? A limit to the validity of the random walk and martingale models, Rev. Econ. Stat, 53(3) (1971) 225{236.
[17] H. K. Liu and J. J. Chang, A closed{form approximation for the fractional Black{Scholes model with transaction costs, Comput. Math. Appl, 65(11) (2013) 1719{1726.
[18] E. J. Kansa and R. E. Carlson. Improved accuracy of multiquadric interpolation using variable shape parameters, Comput. Math. Appl, 24(12) (1992) 99{120.
[19] E. J. Kansa, Multiquadrics{A scattered data approximation scheme with applications to computational  uid{dynamics.I. surface approximations and partial derivative estimates, Comput. Math. Appl, 19(8-9) (1990) 127{145.
[20] Y. K. Kwok, Mathematical models of  nancial derivatives, Second edition. Springer Finance. Springer, Berlin, 2008.
[21] G. Jumarie, Stock exchange fractional dynamics de ned as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional BlackScholes equations, Insurance: Mathematics and Economics, 42 (2008) 271{287.
[22] Z. C. Deng, J. N. Yu and L. Yang, An inverse problem arisen in the zero-coupon bond pricing, Nonlinear Analysis: Real World Applications, 11(3) (2010) 1278{1288
[23] R. Franke, Scattered data interpolation: tests of some methods, Math. Comp, 38(157) (1982) 181{200.
[24] C. S. Huang, C. F. Lee, and A. H. D. Cheng, Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method, Eng. Anal. Bound. Elem, 31(7) (2007) 614{623.
[25] R. E. Carlson and T. A. Foley, The parameter R2 in multiquadric interpolation, Comput. Math Appl, 21(9) (1991) 29{42.
[26] S. A. Sarra and D. Sturgill, A random variable shape parameter strategy for radial basis function approximation methods, Eng. Anal. Bound. Elem, 33(11) (2009) 1239{1245.
[27] J. Xue, Pricing Callable Bonds, (Project Report) Uppsala University, 2011.