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Probabilistic Interpretation of the L and Prabhakar Integrals of Fractional Order |
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PP: 351-355 |
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doi:10.18576/pfda/110209
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Author(s) |
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Marc Jornet,
Juan J. Nieto,
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Abstract |
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| We present a probabilistic interpretation of the L-fractional integration. This integral is the inverse of the known L-fractional derivative. We prove that the fractional integral can be expressed as an expected value of a random variable, which describes dilation or scaling and is related to the beta distribution. The proposed explanation gives the possibility of a generalization of non-integer-order integration and differentiation, by using continuous probability densities. In fact, the general Prabhakar integral operator can be given a probabilistic interpretation as well, in terms of an average, and thus obtain the Riemann-Liouville and L integrals as particular cases.
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