Electronic Communications in Probability

Explicit solutions to fractional differential equations via generalized gamma convolution

Mirko D'Ovidio

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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