In this paper we study the representation of distribution functions of random variables by one-sided fractional Riemann-Liouville integrals. Using the apparatus of classical and fractional analysis, we obtain simple sufficient conditions imposed on fractional analogs of density functions and new properties of the latter, which essentially differ from the usual properties of ordinary density functions. Characteristic features of functions whose fractional integrals correctly represent distribution functions are described.
Topics
Fractional calculus
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