Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica (Nov 2016)

On the Kolmogorov forward equations within Caputo and Riemann-Liouville fractions derivatives

  • Alipour Mohsen,
  • Baleanu Dumitru

DOI
https://doi.org/10.1515/auom-2016-0045
Journal volume & issue
Vol. 24, no. 3
pp. 5 – 19

Abstract

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In this work, we focus on the fractional versions of the well-known Kolmogorov forward equations. We consider the problem in two cases. In case 1, we apply the left Caputo fractional derivatives for α ∈ (0, 1] and in case 2, we use the right Riemann-Liouville fractional derivatives on R+, for α ∈ (1, +∞). The exact solutions are obtained for the both cases by Laplace transforms and stable subordinators.

Keywords