Exact Solution of Fractional Black-Scholes European Option Pricing Equations

We introduce two algorithms in order to find the exact solution of the nonlinearTime-fractional Partial differential equation, in this research work. Thosealgorithms are proposed in the following structure: The Modified HomotopyPerturbation Method (MHPM), The Homotopy Perturbation and SumuduTransform Method. The results achieved using the both methods are thesame. However, we calculate the approached theoretical solution of theBlack-Scholes model in the form of a convergent power series with a regularlycalculated element. Finally, we propose a descriptive example to demonstratethe efficiency and the simplicity of the methods.