Progress in Fractional Differentiation & Applications
Abstract
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.
Digital Object Identifier (DOI)
http://dx.doi.org/10.18576/pfda/050101
Recommended Citation
E. Tarasov, Vasily and S. Tarasova, Svetlana
(2019)
"Probabilistic Interpretation of Kober Fractional Integral of Non-Integer Order,"
Progress in Fractional Differentiation & Applications: Vol. 5:
Iss.
1, Article 1.
DOI: http://dx.doi.org/10.18576/pfda/050101
Available at:
https://digitalcommons.aaru.edu.jo/pfda/vol5/iss1/1
