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By collecting from literature data the experimental evidences of anomalousdiffusion of passive tracers inside cytoplasm, and in particular ofsubdiffusion of mRNA molecules inside live E. coli cells, we get theprobability density function of molecules' displacement and we derive thecorresponding Fokker-Planck equation. Molecules' distribution emerges to berelated to the Kr\"atzel function and its Fokker-Planck equation be afractional diffusion equation in the Erd\'elyi-Kober sense. The irreducibilityof the derived Fokker-Planck equation to those of other literature models isalso discussed.

The Fokker-Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm