In this paper, a new \(\zeta\) -Caputo Fractional Derivative Black-Scholes Model via European Options (CFBSM) has been studied. Moreover, we have proposed a new Numerical Implicit Scheme (NIS) for solving the CFBSM. Also, we studied the stability and the convergence of the NIS. Finally, some numerical experiments are given to compare and show the efficiency of the NIS to other numerical methods for solving fractional Black-Scholes (BS) model. Moreover, by those experiments, we proved the efficiency and the advantages of the CFBSM versus the classical integer-order derivative BS model via European Options.
