Fractional Vasicek Model in Financial Mathematics

In this paper, we proposed a fractional Vasicek model with Riemann-Liouville fractional derivative, which is not discussed in the literature. A systematic investigation is presented to derive an exact solution of the classical and fractional Vasicek model using the invariant subspace method. Using the obtained invariant subspace, we constructed an exact solution in terms of the Mittag-Leffler function. The derived exact solution and the effect of time-fractional order α are shown graphically.