Probability Interpretation of the Integral of Fractional Order

By A. Stanislavsky. 2004

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The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, background): “We note that the connection of the fractional integral with stable distributions was recently investigated explicitly in (Stanislavsky 2004).”
Economic interpretation of fractional derivatives (2017, background): “There are different interpretations of the fractional derivatives and integrals [21]-[36] such as probabilistic interpretations [24]-[26], informatic interpretation [27], geometric interpretations [28]-[30] and [31]-[32], physical interpretations [31]-[32] and [33]-[36].”
Elasticity for economic processes with memory: Fractional differential calculus approach (2016, background): “Derivatives and integrals of non-integer orders have unusual geometric [19], probabilistic [20, 21] and discrete interpretations [22, 23].”