Abstract
The Black-Scholes model is well known for determining the behavior of capital asset pricing models in the finance sector. The present article deals with the Black-Scholes model via the Caputo fractional derivative and Atangana-Baleanu fractional derivative operator in the Caputo sense, respectively. The Jafari transform is merged with the Adomian decomposition method and new iterative transform method. It is worth mentioning that the Jafari transform is the unification of several existing transforms. Besides that, the convergence and uniqueness results are carried out for the aforesaid model. In mathematical terms, the variety of equations and their solutions have been discovered and identified with various novel features of the projected model. To provide additional context for these ideas, numerous sorts of illustrations and tabulations are presented. The precision and efficacy of the proposed technique suggest its applicability for a variety of nonlinear evolutionary problems.