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This paper introduces the Fractional Projected Differential Transform Method (FPDTM) for the solution of the Time-fractional Barrier Option Black-Scholes Pricing Model (TFBOBSPM). The method seeks the solution using sufficient initial (transformed boundary conditions), without any discretization or restrictive assumptions. The efficiency and precision of the proposed methods are tested using illustrative examples. Thus, the FPDTM is suggested for strongly nonlinear differential models with financial applications.

PDTM for the solution of a time-fractional barrier option Black-Scholes model