Abstract
In this paper, we consider an inverse problem for a fractional diffusion equation which is highly ill-posed. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α(0<α<1). We show that the problem is severely ill-posed and further apply an optimal regularization method to solve it based on the solution in the frequency domain. We can prove the optimal convergence estimate, which shows that the regularized solution depends continuously on the data and is a good approximation to the exact solution. Numerical examples show that the proposed method works well.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
