Special Session 65: Nonlinear Evolution Equations and Related Topics

On fractional in time diffusion equations

Ciprian Gal
Florida International University
USA
Co-Author(s):    Mahamadi Warma
Abstract:
This talk provides the introduction to fractional diffusion processes and provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to such fractional (in time) kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators.