[1] M.A. Asiru, Further properties of the Sumudu transform and its applications, International
Journal of Mathematical Education in Science and Technology 33 (2002), 441-449.
[2] G. Barles and H.M. Soner, Option pricing with transaction costs and a nonlinear Black-Scholes
equation, Finance and Stochastics 2 (1998), 369-397.
[3] F.B.M. Belgacem, A.A. Karaballi, Sumudu transform fundamental properties investigations
and applications, Journal of Applied Mathematics and Stochastic Analysis, (2006), 1-23.
[4] T. Bjork and H. Hult, A note on Wick products and the fractional Black-Scholes model,
Finance and Stochastics 9 (2005), 197-209.
[5] C. Castelli. The theory of options in stocks and shares. Fc Mathieson, London, 1877.
[6] Z. Cen and A. Le, A robust and accurate finite difference method for a generalized BlackScholes
equation. J. Comput. Appl. Math, 235 (2011), 3728-3733.
[7] V.B.L. Chaurasia and J. Singh, Application of Sumudu transform in Schodinger equation
occurring in quantum mechanics, Applied Mathematical Sciences 4 (2010), 2843- 2850.
[8] M.H.A. Davis, V.G. Panas, and T. Zariphopoulou, European option pricing with transaction
costs, SIAMJournal on Control and Optimization 31 (1993), 470-493.
[9] K. Diethelm and N.J. Ford, Multi-order fractional differential equations and their numerical
solution, Applied Mathematics and Computation 154 (2004), 621-640.
[10] J.S. Duan, R. Rach, D. Buleanu, and A.M. Wazwaz, A review of the Adomian decomposition
method and its applicaitons to fractional differential equations, Communications in Fractional
Calculus 3 (2012), 73-99.
[11] M.A.M. Ghandehari and M. Ranjbar, A numerical method for solving a fractional partial
differential equation through converting it into an NLP problem, Computers and Mathematics
with Applications. 65 (2013), 975-982.
[12] V. Gulkac, The homotopy perturbation method for the Black-Scholes equation, J. Stat. Comput.
Simul. 80 (2010), 1349-1354.
[13] J.H. He, Approximate analytical solution for seepage flow with fractional derivative in porous
media.Comput. Methods Appl. Mech. Eng. 167 (1998), 57-68.
[14] J.H. He, Variational iteration methoda kind of non-linear analytical technique: some examples,
International Journal of Non-Linear Mechanics 34 (1999), 699-708.
[15] J.C. Hull, Options future and other derivatives. Sixth edition, Pearson prentice Hall, Toronto,
2006.
[16] J.C. Hull and A.D. White, Thepricingof optionsonassetswith stochastic volatilities, Journal
of Finance 42 (1987), 281-300.
[17] M. Inokuti, H. Sekine, T. Mura, General use of the Lagrange multiplier in nonlinear mathematical
physics. In: Nemat-Nassed S, editor. Variational method in the mechanics of solids,
pp. 156-162, Pergamon press, 1978.
[18] X.Y. Jiang and H.T. Qi, Thermal wave model of bioheat transfer with modified RiemannLiouville
fractional derivative, Journal of Physics 45 (2012).
[19] S. Kumar, A. Yildirim, Y. Khan, H. Jafari, K. Sayevand and L. Wey, Analytical solution of
fractional Black-Scholes European option pricing equation by using laplace transform. Journal
of Fractional Calculus and Applications, 2 (2012), 1-9.
[20] J.R. Liang, J. Wang, W.J. Zhang, W.Y. Qiu, and F.Y. Ren, Option pricing of a bi-fractional
Black-Merton-Scholes model with the Hurst exponent H in [1/2,1], Applied Mathematics
Letters 23 (2010), 859-863.
[21] F.W. Liu, V. Anh, and I. Turner, Numerical solutionof the space fractional Fokker-Planck
equation, Journal of Computational and Applied Mathematics 166 (2004), 209-219.
[22] J.H. Ma and Y.Q. Liu, Exact solutions for a generalized nonlinear fractional Fokker-Planck
equation, Nonlinear Analysis. RealWorld Applications 11 (2010), 515-521.
[23] R.C. Merton, On the pricing of corporate debt: the risk structure of interest rates, Journal
of Finance 29 (1974), 449- 470.
[24] R.C. Merton, Option pricing when underlying stock returns are discontinuous, Journal of
Financial Economics, 3 (1976), 125-144.
[25] F. Mainardi, On the initial value problem for the fractional diffusion-wave equation, in: S.
Rionero, T. Ruggeeri, Waves and stability in continuous media, World scientific, Singapore ,
1994.
[26] I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering,
Academic Press, San Diego, Calif, USA, 1999.
[27] X.T. Wang, Scaling and long-range dependence in option pricing I: Pricing European option
with transaction costs under the fractional Black-Scholes model, Physica A 389 (2010), 438-
444.
[28] G.C. Wu, D. Baleanu, Variational iteration method for the Burgers flow with fractional
derivatives-New Lagrange multipliers, Applied Mathematical Modelling 37 (2013), 6183-6190.
)
