The physical mechanism responsible for the high viscosity in accretion disks is still under debate. The parameterization of the viscous stress as αP proved to be a successful representation of this mechanism in the outer parts of the disk, explaining the dwarf novae and X-ray novae outbursts as being due to ionization instability. We show that this parameterization can also be adopted in the innermost part of the disk where the adoption of the α-viscosity law implies the presence of the instability in the radiation pressure-dominated region. We study the time evolution of such disks. We show that the time-dependent behavior of GRS 1915+105 can be well reproduced if the α-viscosity disk model is calculated accurately (with proper numerical coefficients in vertically averaged equations and with advection included) and if the model is supplemented with (1) a moderate corona dissipating 50% of energy and (2) a jet carrying a luminosity-dependent fraction of energy. These necessary modifications in the form of the presence of a corona and a jet are well justified observationally. The model predicts outbursts at a luminosity larger than 0.16Edd, as required, and correct outburst timescales and amplitudes, including the effect of an increasing outburst timescale with mean luminosity. This result strongly suggests also that the α-viscosity law is a good description of the actual mechanism responsible for angular momentum transfer in the innermost, radiation pressure-dominated part of the disk around a black hole.