Planet migration originally refers to protoplanetary disks, which are more massive and dense than typical accretion disks in binary systems. We study planet migration in an accretion disk in a binary system consisting of a solar-like star hosting a planet and a red giant donor star. The accretion disk is fed by a stellar wind. %, disk self-gravity is neglected. We use the $alpha$-disk model and consider that the stellar wind is time-dependent. Assuming the disk is quasi-stationary we calculate its temperature and surface density profiles. In addition to the standard disk model, when matter is captured by the disk at its outer edge, we study the situation when the stellar wind delivers matter on the whole disc surface inside the accretion radius with the rate depending on distance from the central star. Implying that a planet experiences classical type I/II migration we calculate migration time for a planet on a circular orbit coplanar with the disk. Potentially, rapid inward planet migration can result in a planet-star merger which can be accompanied by an optical or/and UV/X-ray transient. We calculate timescale of migration for different parameters of planets and binaries. Our results demonstrate that planets can fall on their host stars within the lifetime of the late-type donor for realistic sets of parameters.
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