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Probabilistic Interpretation of Kober Fractional Integral of Non-Integer Order |
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PP: 1-5 |
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doi:10.18576/pfda/050101
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Author(s) |
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Vasily E. Tarasov,
Svetlana S. Tarasova,
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Abstract |
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| In this paper, probabilistic interpretation of the Kober fractional integration of non-integer order is proposed. We prove that
the fractional integral, which is proposed by Kober, can be interpreted as an expected value of a random variable up to a constant
factor. In this interpretation, the random variable describes dilation (scaling), which has the gamma distribution. The Erdelyi-Kober
fractional integration also has a probabilistic interpretation. Fractional differential operators of Kober and Erdelyi-Kober type have
analogous probabilistic interpretation. The proposed interpretation leads to a possibility of generalization of the fractional integration
and differentiation by using continuous probability distributions. |
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