Electronic Communications in Probability

Explicit solutions to fractional differential equations via generalized gamma convolution

Mirko D'Ovidio

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Abstract

In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional diffusion equations involving the adjoint operators of a square Bessel process and a Bessel process

Article information

Source
Electron. Commun. Probab., Volume 15 (2010), paper no. 42, 457-474.

Dates
Accepted: 4 October 2010
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465243985

Digital Object Identifier
doi:10.1214/ECP.v15-1570

Mathematical Reviews number (MathSciNet)
MR2726092

Zentralblatt MATH identifier
1226.60109

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60J60: Diffusion processes [See also 58J65] 26A33: Fractional derivatives and integrals

Keywords
Mellin convolution formula generalized Gamma r.v.'s Stable subordinators Fox functions Bessel processes Modified Bessel functions

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

D'Ovidio, Mirko. Explicit solutions to fractional differential equations via generalized gamma convolution. Electron. Commun. Probab. 15 (2010), paper no. 42, 457--474. doi:10.1214/ECP.v15-1570. https://projecteuclid.org/euclid.ecp/1465243985


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