ABSTRACT Many types of fractional stochastic differential equation (FrSDE), such as Caputo, fractional Brown motion derivatives, and Mittag-Later functions, exist. In recent decades, FrSDE has been a hot topic and can be applied to many fields of research, such as disease transmission, option pricing, and quantitative finance. FrSDEs have various research and applications in financial markets. After comparing many internationally known articles, the fractional order stochastic differential equation proposed in 2016 is most suitable for European option pricing. Over the years, many scholars have studied fractional Brownian motion, fractional ordinary differential equations, and backward differential equations, and no one has studied the application of fractional backward equations in the financial field. Therefore, in this article, to adapt to the financial market more accurately, we construct a backward equation for this kind of FrSDE and construct a new mapping and use the norm method to prove the existence, uniqueness, and stability of the solution to the backward equation. Finally, considering European call options, the Euler Maruyama simulation example of FrSDE is investigated.