Trends in Applied Sciences Research1819-35792151-7908Science International10.3923/tasr.2020.110.114FadugbaS.E. EdogbanyaO.H. 22020152Background and Objectives: This research presents series solution of time-fractional Black-Scholes partial differential equation with boundary condition for a European option pricing problem in a Caputo sense. The aim of this study was to conduct the comparison of two semi-analytical methods namely the Fractional Reduced Differential Transform Method (FRDTM) and the Fractional Laplace Transform Homotopy Perturbation Method (FLTHPM) for the solution of the time-fractional Black-Scholes equation. Materials and Methods: These two methods are based on trans forms involving fractional derivatives. Both methods provide a closed-form solution in the form of a convergent series with easily computable components, require no restrictive assumptions. The methods are compared on time-fractional Black-Scholes equation. Results: The solution generated by FRDTM is in excellent agreement with that of FLTHPM. The small size of calculation in FRDTM in comparison with FLTHPM is its advantage. Conclusion: Hence, FRDTM is strongly recommended for the solution of time-fractional Black-Scholes equation emanating from financial market.]]>Black, F. and M. Scholes,197381637654Bohner, M., F.H.M. Sánchez and S. Rodríguez,201497585Baleanu, D., K. Diethelm, E. Scalas and J.J. Trujillo,2016Company, R., E. Navarro, J.R. Pintos and E. Ponsoda,200856813821Jumarie, G.,20105911421164Kumar, S., A. Yildirim, Y. Khan, H. Jafari, K. Sayevand and L. Wei,2012219Kumar, S., D. Kumar and J. Singh,20141177183Keskin, Y. and G. Oturanc,200910741750Keskin, Y. and G. Oturanc,201015382393Keskin, Y. and G. Oturanc,20101207217Keskin, Y. and G. Oturanc,201034113122Acan, O., M.M. Al Qurashi and D. Baleanu,20171052305238Podlubny, I.,1999Vol. 198.Srivastava, V.K., M.K. Awasthi and M. Tamsir,20132013Miller, K.S. and B. Ross,1993Pages: 366Pages: 366Gulkac, V.,20108013491354He, J.H.,200526695700