This research aims to accomplish an analytic solution to mathematical models involving space-time fractional differential equations in the conformable sense in series form through the weighted inner product and separation of variables method. The main advantage of this method is that various linear problems of any kind of differential equations can be solved by using this method. First, the corresponding eigenfunctions are established by solving the Sturm-Liouville eigenvalue problem. Secondly, the coefficients of the eigenfunctions are determined by employing weighted inner product and initial condition. Thirdly, the analytic solution to the problem is constructed in the series form. Finally, an illustrative example is presented to show how this method is implemented for fractional problems and exhibit its effectiveness and accuracy.