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In this paper we discuss fractional generalizations of the filtering problem.The "fractional" nature comes from time-changed state or observation processes,basic ingredients of the filtering problem. The mathematical feature of thefractional filtering problem emerges as the Riemann-Liouville fractionalderivative in the associated Zakai equation. We discuss fractionalgeneralizations of the filtering problem whose state and observation processesare driven by time-changed Brownian motion or/and L\'evy process.

Fractional nonlinear filtering problems and their associated fractional Zakai equations