Hahn hybrid functions for solving distributed order fractional Black–Scholes European option pricing problem arising in financial market

چکیده مقاله

The main purpose of this work is to present a new numerical method based on Hahn hybrid functions (HHFs) for solving of Black–Scholes option pricing distributed order time-fractional partial differential equation. To this end, HHFs are introduced and their fractional integral operator with some properties of HHFs is calculated. In the next, with the help of fractional integral operator of HHFs, Gauss–Legendre quadrature formula and collocation method, distributed order time-fractional Black–Scholes model is reduced to a system of algebraic equations. Furthermore, convergence analysis of the mentioned scheme is discussed. Finally, some test problems have been included to confirm the validity and efficiency of the mentioned numerical scheme. Moreover, Black–Scholes equations are studied through a bibliometric viewpoint. © 2022 John Wiley & Sons, Ltd.