| Summary: | A random walk on a two dimensional square in <inline-formula><math display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> space with a hidden absorbing fractal set <inline-formula><math display="inline"><semantics><msub><mi>F</mi><mi>μ</mi></msub></semantics></math></inline-formula> is considered. This search-like problem is treated in the framework of a diffusion–reaction equation, when an absorbing term is included inside a Fokker–Planck equation as a reaction term. This macroscopic approach for the 2D transport in the <inline-formula><math display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> space corresponds to the comb geometry, when the random walk consists of 1D movements in the <i>x</i> and <i>y</i> directions, respectively, as a direct-Cartesian product of the 1D movements. The main value in task is the first arrival time distribution (FATD) to sink points of the fractal set, where travelling particles are absorbed. Analytical expression for the FATD is obtained in the subdiffusive regime for both the fractal set of sinks and for a single sink.
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