## Electronic Communications in Probability

### Explicit solutions to fractional differential equations via generalized gamma convolution

Mirko D'Ovidio

#### 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

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

Rights

#### 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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