In this seminar I will present some recent results obtained in collaboration with J.L. Vazquez on a fractional thin film equation. This is a degenerate parabolic equation of order $/alpha$ with $/alpha/in [2,4]$ that interpolates between the standar porous medium equation ($/alpha=2$) and the thin film equation ($/alpha=4$). We prove existence of nonnegative properly defined weak solution and we construct compactly supported self similar solutions.