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Abstract
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In this paper two di erent 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 di erential 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 nancial derivatives. This methods
nds 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.
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