on the gegenbaur pseudospectral method for the time fractional black-scholes european option pricing model

Abstract. the time fractional black–scholes model(tfbsm) is employed to priceamerican or european call and put options on a stock paying on a non-dividend basis.in this paper, we examine pseudospectral method for numerical solution of tfbsm,based on gegenbauer polynomials and chebyshev spectral differentiation matrix . thepresented method reduces tfbsm to a generalized sylvester matrix equation, which canbe solved by the global gmres method.