Fractional Diffusion in Gaussian Noisy Environment

Fractional Diffusion in Gaussian Noisy Environment

We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: \(D_t^{(\alpha)} u(t, x)=\textit{B}u+u\cdot \dot W^H\), where \(D_t^{(\alpha)}\) is the Caputo fractional derivative of order \(\alpha\in (0,1)\) wi...

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Bibliographic Details
Main Authors: Guannan Hu, Yaozhong Hu
Format: Article
Language:English
Published: MDPI AG 2015-03-01
Series:Mathematics
Subjects:
fractional derivative
fractional order stochastic heat equation
mild solution
time homogeneous fractional Gaussian noise
stochastic integral of the Itô type
multiple integral of the Itô type
chaos expansion
Fox's H-function
Green's functions
Online Access:http://www.mdpi.com/2227-7390/3/2/131

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http://www.mdpi.com/2227-7390/3/2/131

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