Well-posedness of Generalized Fractional Singular Burgers equation driven by $\mathrm{\mid }D{\mathrm{\mid }}^{\frac{1}{2}}\xi$

In this paper, we study the generalized solution of Fractional Singular Burgers equation driving by $\mathrm{\mid }D{\mathrm{\mid }}^{\frac{1}{2}}\xi$. We establish a framework to describe the equations satisfied by generalized solutions, termed the Generalized Fractional Singular Burgers equation(GFSB), and prove its local well-posedness. Finally, we prove that the solution of GFSB can be the generalized solution of Fractional Singular Burgers equation for $\gamma >\frac{3}{2}$.