Solvability and Mittag–Leffler stability analysis for time fractional partial differential equations

We present a class of time fractional partial differential equations with Dirichlet boundary conditions. The main result shows the existence theorem of the proposed model using the Faedo–Galerkin method with some compactness arguments. Moreover, we prove the Mittag–Leffler stability of solutions of the considered model.
Keywords: fractional PDE, weak solution, Faedo–Galerkin method, Mittag–Leffler stability.