Drifted Brownian motions governed by fractional tempered derivatives
Volume 5, Issue 4 (2018), pp. 445–456
Pub. online: 19 September 2018
Type: Research Article
Open Access
Open Access
Received
24 April 2018
24 April 2018
Revised
28 June 2018
28 June 2018
Accepted
29 August 2018
29 August 2018
Published
19 September 2018
19 September 2018
Abstract
Fractional equations governing the distribution of reflecting drifted Brownian motions are presented. The equations are expressed in terms of tempered Riemann–Liouville type derivatives. For these operators a Marchaud-type form is obtained and a Riesz tempered fractional derivative is examined, together with its Fourier transform.
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