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Abstract
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In this paper, a new identification of the Lagrange multipliers by means of the
Sumudu transform, is employed to obtain a quick and accurate solution to the frac-
tional Black-Scholes equation with the initial condition for a European option pricing
problem. Undoubtedly this model is the most well known model for pricing financial
derivatives. The fractional derivatives is described in Caputo sense. This method
finds the analytical solution without any discretization or additive assumption. The
analytical method has been applied in the form of convergent power series with eas-
ily computable components. Some illustrative examples are presented to explain the
efficiency and simplicity of the proposed method.
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