Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method

In this study, we use a new approach, known as the Aboodh residual power series method (ARPSM), in order to obtain analytical results of Black–Scholes differential equations (BSDEs), which are prime for judgment European call and put options on non-dividend-paying stock, especially when they consist time-fractional derivatives. The fractional derivative is considered Caputo sense. This approach combination transform (RPSM). suggested based version Taylor’s that generates convergent solution. advantage our strategy can operator equation into an algebraic equation, decreases amount computation required solution subsequent step. primary aspect proposed how easily it computes coefficients terms using simple limit at infinity concept. RPSM, unknown solutions must be determined derivative, other well-known approximate approaches like variational iteration, Adomian decomposition, homotopy perturbation require integration operators, challenging case. Moreover, solves problems without need He’s polynomials polynomials, so small size strength over various methods. efficiency verified by graphs numerical data. recurrence errors levels utilized demonstrate convergence evidence approximative exact comparison study established absolute solutions. We come conclusion apply accurate findings.