Unique recovery of the initial state of distributed order time fractional diffusion equation

Year 2024, Early Access, 1 - 15

Hui Liu Zhiyuan Li , Zhousheng Ruan

https://doi.org/10.15672/hujms.1285069

Abstract

We use Phragm\'en-Lindel\"of-Liouville argument to prove the uniqueness for the determining the initial state of solution for the time fractional diffusion equation with distributed order derivative. Several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Keywords

ultraslow diffusion, inverse problem, regularization method

Supporting Institution

National Natural Science Foundation of China

Project Number

12271277; 12061008

References

• [1] D. Araya and C. Lizama, Almost automorphic mild solutions to fractional differential equations, Nonlinear Analysis Theory Methods and Applications, 69(11), 3692–3705, 2008.