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

Mohsen Alipour; Dumitru Baleanu

doi:10.1515/auom-2016-0045

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 24 (2016): Issue 3 (November 2016)

By: Mohsen Alipour and Dumitru Baleanu

Open Access

|Sep 2017

Abstract

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.

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Articles in this issue

DOI: https://doi.org/10.1515/auom-2016-0045 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 5 - 19

Submitted on: Jun 20, 2015

Accepted on: Sep 25, 2015

Published on: Sep 21, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Caputo fractional derivative,

Riemann-Liouville fractional derivative,

Mittag-Leffler functions,

Fractional Kolmogorov forward equations,

Stable subordinator

Related subjects:

Mathematics,

General mathematics

© 2017 Mohsen Alipour, Dumitru Baleanu, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 24 (2016): Issue 3 (November 2016)