Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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FRACTIONAL EULER'S INTEGRAL OF FIRST AND SECOND KINDS. APPLICATION TO FRACTIONAL HERMITE'S POLYNOMIALS AND TO PROBABILITY DENSITY OF FRACTIONAL ORDER

  • Jumarie, Guy (Department of Mathematics, University of Quebec at Montreal)
  • Published : 2010.01.30
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Abstract

One can construct a theory of probability of fractional order in which the exponential function is replaced by the Mittag-Leffler function. In this framework, it seems of interest to generalize some useful classical mathematical tools, so that they are more suitable in fractional calculus. After a short background on fractional calculus based on modified Riemann Liouville derivative, one summarizes some definitions on probability density of fractional order (for the motive), and then one introduces successively fractional Euler's integrals (first and second kind) and fractional Hermite polynomials. Some properties of the Gaussian density of fractional order are exhibited. The fractional probability so introduced exhibits some relations with quantum probability.

Keywords

References

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