A New Version of Black-Scholes Equation Presented by Time-Fractional Derivative

In this article, a new time-fractional order Black-Scholes equation has been derived. In this derivation, the asset price satisfies in a fractional order stochastic differential equation. Here, the effect of trend memory in financial pricing is considered. Finally, a new approximate analytical method has been used to solve our new proposed time-fractional Black-Scholes equation.