Analysis and dynamics of the Ivancevic option pricing model with a novel fractional calculus approach

Abstract

The aim of the current study is to capture the complex behavior of the Ivancevic option pricing (IOP) model using the -homotopy analysis transform method (-HATM) with novel fractional operator. The generalization of the Black-Scholes model with the nonlinear Schrödinger equation plays a pivotal role in financial mathematics in studying the option-pricing wave function associated with two parameters. Based on adaptive market potential and volatility constant with distinct initial situations, we hired three distinct cases to exemplify the ability of -HATM. The considered method is elegant unification of the -homotopy analysis and Laplace transform algorithms. The derivative of fractional order is projected with the Atangana-Baleanu (AB) operator. The fixed-point theorem is used to present the existence and uniqueness of the attained result for the considered model, and we hire five distinct initial conditions. The hired scheme is highly methodical and exact to analyze the insights of the complex system with integer and fractional order exemplifying associated areas of science, which can be observed using plots and table.