Fractional Diffusion in Gaussian Noisy Environment

Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness of the solution and calculate the moment bounds of the solution when the noise has Reisz kernel as space covariance. Along the way, we obtain some new properties of the fundamental solutions. Chapter 4 studies the time-fractional diffusion with fractional Gaussian noise. We obtain conditions so that the square integrable solution exists uniquely. Chapter 5 studies the time-fractional diffusion where the Gaussian noise is general in time with space covariance given by fractional, Riesz and Bessel kernel.

Grantor dc:publisher

University of Kansas

Year dc:date.issued

2015

Author dc:creator

• Hu, Guannan

Advisor dc:contributor.advisor

• Hu, Yaozhong

• Mathematics
• chaos expansion
• Fox's H-function;
• fractional derivative
• Green's functions
• mild solution
• multiple integral of the Itô type

Statement dc:rights

• Copyright held by the author.

Language dc:language.iso

en

Dc Identifier Other

http://dissertations.umi.com/ku:14276

OAI identifier oai:identifier

oai:kuscholarworks.ku.edu:1808/21696