<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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<sub>+</sub>, for α ∈ (1, +∞). The exact solutions are obtained for the both cases by Laplace transforms and stable subordinators.</p></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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Published Online: Sep 21, 2017

Page range: 5 - 19

Received: Jun 20, 2015

Accepted: Sep 25, 2015

DOI: https://doi.org/10.1515/auom-2016-0045

Keywords
Caputo fractional derivative, Riemann-Liouville fractional derivative, Mittag-Leffler functions, Fractional Kolmogorov forward equations, Stable subordinator

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Sep 21, 2017

Page range: 5 - 19

Received: Jun 20, 2015

Accepted: Sep 25, 2015

DOI: https://doi.org/10.1515/auom-2016-0045

KeywordsCaputo fractional derivative, Riemann-Liouville fractional derivative, Mittag-Leffler functions, Fractional Kolmogorov forward equations, Stable subordinator

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Caputo fractional derivative, Riemann-Liouville fractional derivative, Mittag-Leffler functions, Fractional Kolmogorov forward equations, Stable subordinator