In this article, we consider a general time-fractional differential equation, (∂$^α$v/∂$^t$α) =F[x, v, v$_x$, v$_{xx}$, v$_{xxx}$ ], where F is a third-order polynomial operator with quadratic nonlinearities. We describe the operator F which admits two-dimensional invariant subspaces which are solutions of second-order ordinary differential equation with constant coefficients. Using the invariant subspace method, we find explicit solution for fractional differential equations for various cases of operator F. We show that explicit solutions to many of the known equations like time-fractional Rosenau–Hyman equation, Korteweg–de Vries equation, Benjamin equationetc. can be derived using this method.