barrier options pricing of fractional version of the black-scholes ‎model‎

in this paper two different methods are presented to approximate the solution of the fractional black-scholes equation for valuation of barrier option. also, the two schemes need less computational work in comparison with the traditional methods. in this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the application of this methods for pricing barrier options of fractional version of the black-scholes model. undoubtedly this model is the most well known model for pricing financial derivatives. this methods finds the analytical solution without any discretization or additive assumption. the approximate analytic solution is calculated in the form of convergent series with easily computable components, to solve the fractional black-scholes ‎equation.