Series form solutions of time–space fractional Black–Scholes model via extended He-Aboodh algorithm

The objective of the current study is analyze linear and nonlinear time–space fractional Black–Scholes models via modified homotopy perturbation method (m-HPM). In current investigation, memory effects in financial markets are explored through fractional derivative in Caputo sense. The effectiveness of proposed methodology is checked numerically by finding residual errors and presented in tables. These tables also provide a benchmark for the comparison with already existing results in literature. Furthermore, solutions are graphically analyzed via 3D and contour plots across a range of parameters under varying market conditions. Analysis confirms the efficiency of m-HPM for predicting solutions of time–space fractional Black–Scholes models. The current study can contribute in understanding the applications of fractional calculus in finance, and can be a valuable computational tool for pricing financial derivatives in fractional environments.