Nonlocal time porous medium equation with fractional time derivative

We consider nonlinear nonlocal diffusive evolution equations, governed by a Lévy-type nonlocal operator, fractional time derivative and involving porous medium type nonlinearities. Existence and uniqueness of weak solutions are established using approximating solutions and the theory of maximal monotone operators. Using the De Giorgi–Nash–Moser technique, we prove that the solutions are bounded and Hölder continuous for all positive time.