Fractional Probability Theory of Arbitrary Order

Автор: Tarasov Vasily E.
Журнал: Fractal and Fractional
Том: 7
Номер: 2
Год издания: 2023
Издательство: MDPI Publishing
Местоположение издательства: Basel, Switzerland, Switzerland
Номер статьи: 137
DOI: 10.3390/fractalfract7020137
Аннотация: A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability density function (fractional PDF) is proposed. The basic properties of the fractional PDF are proven. The definition of the fractional cumulative distribution function (fractional CDF) is also suggested, and the basic properties of these functions are also proven. It is proven that the proposed fractional cumulative distribution functions generate unique probability spaces that are interpreted as spaces of a fractional probability theory of arbitrary order. Various examples of the distributions of the fractional probability of arbitrary order, which are defined on finite intervals of the real line, are suggested.
Добавил в систему: Тарасов Василий Евгеньевич

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