Application of the Generalized Laplace Homotopy Perturbation Method to the Time-Fractional Black–Scholes Equations Based on the Katugampola Fractional Derivative in Caputo Type

In the finance market, Black–Scholes equation is used to model price change of underlying fractal transmission system. Moreover, fractional differential equations recently are accepted by researchers that a powerful tool in studying geometry and dynamics. Fractional modeling various important situations or phenomena real world such as fluid flow, acoustics, electromagnetic, electrochemistry material science. There an question finance: “Can be applied financial market?”. The answer “Yes”. Due self-similar property derivative, it can reply long-range dependence better than integer-order derivative. Thus, these advantages beneficial manage structure market. this article, classical with two assets for European call option modified replacing order ordinary derivative Caputo type Katugampola sense. analytic solution time-fractional pricing derived using generalized Laplace homotopy perturbation method. method combination transform. carried out form Mittag–Leffler function. Finally, effects fractional-order shown.