DETERMINATION OF A NONLINEAR COEFFICIENT IN A TIME-FRACTIONAL DIFFUSION
EQUATION
- Mustafa Zeki,
- Ramazan Tinaztepe,
- Salih Tatar,
- Suleyman Ulusoy
Mustafa Zeki
American University of the Middle East
Corresponding Author:mustafa.zeki@aum.edu.kw
Author ProfileAbstract
Direct and inverse problems for a nonlinear time fractional equation are
studied. It is proved that the direct problem has a unique weak solution
and the solution depends continuously on the nonlinear coefficient. Then
it is shown that the inverse problem has a quasi-solution. The direct
problem is solved by method of lines using an operator approach. A
quasi-Newton optimization method is used for the numerical solution to
the inverse problem. Tikhonov regularization is used to overcome the
ill-posedness of the inverse problem. Numerical examples with noise free
and noisy data illustrate applicability and accuracy of the proposed
method to some extent.