An inverse source problem for a two dimensional time fractional diffusion equation with nonlocal boundary conditions

作者：Kirane Mokhtar; Malik Salman A^*; Al Gwaiz Mohammed A

来源：Mathematical Methods in the Applied Sciences, 2013, 36(9): 1056-1069.

DOI：10.1002/mma.2661

• inverse problem
• fractional derivative
• diffusion equation
• integral equations
• biorthogonal system of functions
• Fourier series

We consider the inverse source problem for a time fractional diffusion equation. The unknown source term is independent of the time variable, and the problem is considered in two dimensions. A biorthogonal system of functions consisting of two Riesz bases of the space L2[(0,1)x(0,1)], obtained from eigenfunctions and associated functions of the spectral problem and its adjoint problem, is used to represent the solution of the inverse problem. Using the properties of the biorthogonal system of functions, we show the existence and uniqueness of the solution of the inverse problem and its continuous dependence on the data.

• 出版日期2013-6